Midterm Practice 1
A random experiment with three outcomes has been repeated 50 times, and it was learned that E1 occurred 10 times, E2 occurred 13 times, and E3 occurred 27 times. Assign probabilities to the following outcomes for E1, E2 and E3. Round your answer to two decimal places.
A random experiment with three outcomes has been repeated 50 times, and it was learned that E1 occurred 10 times, E2 occurred 13 times, and E3 occurred 27 times. Assign probabilities to the following outcomes for E1, E2 and E3. Round your answer to two decimal places. P(E1) 0.2 P(E2) 0.26 P(E3) 0.54 What method did you use? relative frequency
A technician services mailing machines at companies in the Phoenix area. Depending on the type of malfunction, the service call can take 1.1, 2.3, 3.1, or 4.1 hours. The different types of malfunctions occur at the same frequency. If required, round your answers to two decimal places.
Develop a probability distribution for the duration of a service call. Duration of Call x f(x) 1.1 0.25 2.3 0.25 3.1 0.25 4.1 0.25 1.00 Does this probability distribution satisfy equation (5.1)? yes, all probability functions are greater than zero Does this probability distribution satisfy equation (5.2)? yes, it equals zero What is the probability a randomly selected service call will take 3.1 hours? 0.25 A service call has just come in, but the type of malfunction is unknown. It is 3:00 P.M. and service technicians usually get off at 5:00 P.M. What is the probability the service technician will have to work overtime to fix the machine today? 0.75
Three students scheduled interviews for summer employment at an Institute. In each case the interview results in either an offer for a position or no offer. Experimental outcomes are defined in terms of the results of the three interviews.
How many experimental outcomes exist? 8 Let x equal the number of students who receive an offer. Is x continuous or discrete? Show the value of the random variable x, where x is the number of yeses. Let Y = "Yes, the student receives an offer", and N = "No, the student does not receive an offer." Experimental Outcome Value of x (N, Y, N) 1 (Y, N, Y) 2 (Y, N, N) 1 (N, Y, Y) 2 (Y, Y, N) 2 (N, N, Y) 1 (N, N N) 0 (Y, Y, Y) 3
A questionnaire provides 66 Yes, 33 No, and 21 no-opinion answers.
In the construction of a pie chart, how many degrees would be in the section of the pie showing the Yes answers? 198 degrees How many degrees would be in the section of the pie showing the No answers? 99 degrees If you constructed a pie chart, what percentage of the circle that would be occupied by each response. Round answers to one decimal place. Yes 55 % No 27.5 % No Opinion 17.5 %
The probability distribution for the random variable x follows. x f(x) 20 0.24 24 0.16 32 0.28 36 0.32
Is this a valid probability distribution? What is the probability that x = 32 (to 2 decimals)? 0.28 What is the probability that x is less than or equal to 24 (to 2 decimals)? 0.40 What is the probability that x is greater than 32 (to 2 decimals)? 0.32
The budgeting process for a midwestern college resulted in expense forecasts for the coming year (in $ millions) of $9, $10, $11, $12, and $13. Because the actual expenses are unknown, the following respective probabilities are assigned: 0.29, 0.15, 0.22, 0.12, and 0.22.
Show the probability distribution for the expense forecast. x f(x) 9 .29 10 .15 11 .22 12 .12 13 .22 What is the expected value of the expense forecast for the coming year (to 2 decimals)? 10.83 What is the variance of the expense forecast for the coming year (to 2 decimals)? 2.28 If income projections for the year are estimated at $12 million, how much profit does the college expect to make (report your answer in millions of dollars, to 2 decimals)? 1.17
Refer to the KP&L sample points and sample point probabilities in Tables 4.2 and 4.3.
TABLE 4.2 COMPLETION RESULTS FOR 40 KP&L PROJECTS Completion Time (months) Stage 1 Design Stage 2 Construction Sample point Number of Past Projects Having These Completion Times 2 6 ( 2, 6) 4 2 7 ( 2, 7) 6 2 8 (2, 8) 2 3 6 (3, 6) 2 3 7 (3, 7) 6 3 8 (3, 8) 2 4 6 (4, 6) 2 4 7 (4, 7) 2 4 8 (4, 8) 14 Total 40 Table 4.3 PROBABILITY ASSIGNMENTS FOR THE KP&L PROJECT BASED ON THE RELATIVE FREQUENCY METHOD Sample point Project Completion Time Probability of Sample Point (2, 6) 8 months P(2, 6)=4/40=0.1 (2, 7) 9 months P(2, 7)=6/40=0.15 (2, 8) 10 months P(2, 8)=2/40=0.05 (3, 6) 9 months P(3, 6)=2/40=0.05 (3, 7) 10 months P(3, 7)=6/40=0.15 (3, 8) 11 months P(3, 8)=2/40=0.05 (4, 6) 10 months P(4, 6)=2/40=0.05 (4, 7) 11 months P(4, 7)=2/40=0.05 (4, 8) 12 months P(4, 8)=14/40=0.35 Total 1.00 The design stage (stage 1) will run over budget if it takes 4 months to complete. List the sample points in the event the design stage is over budget. What is the probability that the design stage is over budget (to 2 decimal)? 0.45 The construction stage (stage 2) will run over budget if it takes 8 months to complete. List the sample points in the event the construction stage is over budget. What is the probability that the construction stage is over budget (to 2 decimals)? 0.45 What is the probability that both stages are over budget (to 2 decimals)? 0.35
The results of a national survey showed that on average, adults sleep 6.9 hours per night. Suppose that the standard deviation is 1.4 hours. Round your answers to the nearest whole number.
Use Chebyshev's theorem to calculate the percentage of individuals who sleep between 4.1 and 9.7 hours. At least 75 % Use Chebyshev's theorem to calculate the percentage of individuals who sleep between 3.9 and 9.9 hours. At least 78 % Assume that the number of hours of sleep follows a bell-shaped distribution. Use the empirical rule to calculate the percentage of individuals who sleep between 4.1 and 9.7 hours per day. 95 % How does this result compare to the value that you obtained using Chebyshev's theorem in part (a)?
he following frequency distribution shows the price per share for a sample of 30 companies listed on the New York Stock Exchange. Price per Share Frequency $20-29 5 $30-39 7 $40-49 4 $50-59 2 $60-69 6 $70-79 2 $80-89 4
ompute the sample mean price per share and the sample standard deviation of the price per share for the New York Stock Exchange companies (to 2 decimals). Assume there are no price per shares between 29 and 30, 39 and 40, etc. Sample mean $ 50.83 Sample standard deviation $ 20.59
A random experiment with three outcomes has been repeated 50 times, and it was learned that E1 occurred 10 times, E2 occurred 12 times, and E3 occurred 28 times. Assign probabilities to the following outcomes for E1, E2 and E3. Round your answer to two decimal places.
(E1) 0.2 P(E2) 0.24 P(E3) 0.56 What method did you use? relative frequency
Figure 1.11 provides a bar chart showing the amount of federal spending for the years 2004 to 2010 (Congressional Budget Office website, May 15, 2011).
. What is the variable of interest? Federal Spending b. Are the data categorical or quantitative? Quantitative c. Are the data time series or cross-sectional? Time series d. Comment on the trend in federal spending over time. How much did the federal government spend in 2010? $ 3.4 trillions (to 1 decimal)
Suppose N = 10 and r = 4. Compute the hypergeometric probabilities for the following values of n and x. If the calculations are not possible, please select "not possible" from below drop-downs, and enter 0 in fields. Round your answers, if necessary.
. n = 4, x = 1 (to 2 decimals). 0.38 b. n = 2, x = 2 (to 3 decimals). 0.133 c. n = 2, x = 0 (to 4 decimals). 0.3333 d. n = 4, x = 3 (to 2 decimals). 0.11 e. n = 5, x = 5 (to 2 decimals). 0
A regional director responsible for business development in the state of Pennsylvania is concerned about the number of small business failures. If the mean number of small business failures per month is 10.7, what is the probability that exactly 4 small businesses will fail during a given month (to 4 decimals)? Assume that the probability of a failure is the same for any two months and that the occurrence or nonoccurrence of a failure in any month is independent of failures in any other month.
0.0123
A regional director responsible for business development in the state of Pennsylvania is concerned about the number of small business failures. If the mean number of small business failures per month is 8.9, what is the probability that exactly 4 small businesses will fail during a given month (to 4 decimals)? Assume that the probability of a failure is the same for any two months and that the occurrence or nonoccurrence of a failure in any month is independent of failures in any other month.
0.0357
Consider a sample with a mean of 60 and a standard deviation of 4. Use Chebyshev's theorem to determine the percentage of the data within each of the following ranges (to the nearest whole number).
50 to 70, at least 84 % 35 to 85, at least 97 % 51 to 69, at least 80 % 48 to 72, at least 89 % 44 to 76, at least 94 %
Consider a sample with data values of 27, 25, 22, 15, 30, 34, 29, and 25. Compute the 20th, 25th, 65th, and 75th percentiles (to 1 decimal, if decimals are necessary).
20th percentile 20.6 25th percentile 22.75 65th percentile 28.7 75th percentile 29.75 `
Consider the following data and corresponding weights.
3.8 6 4.0 4 1.5 1 2.0 9 a. Compute the weighted mean (to 3 decimals). 2.915 b. Compute the sample mean of the four data values without weighting (to 3 decimals). 2.825
Consider a sample with a mean of 60 and a standard deviation of 5. Use Chebyshev's theorem to determine the percentage of the data within each of the following ranges (to the nearest whole number).
40 to 80, at least 75 % 45 to 75, at least 88 % 51 to 69, at least 30 % 48 to 72, at least 17 % 42 to 78, at least 7.7 %
Consider a sample with a mean of 60 and a standard deviation of 5. Use Chebyshev's theorem to determine the percentage of the data within each of the following ranges (to the nearest whole number).
40 to 80, at least 94 % 45 to 75, at least 89 % 51 to 69, at least 69 % 48 to 72, at least 83 % 42 to 78, at least 92 %
Simple random sampling uses a sample of size n from a population of size N to obtain data that can be used to make inferences about the characteristics of a population. Suppose that, from a population of 65 bank accounts, we want to take a random sample of five accounts in order to learn about the population. How many different random samples of five accounts are possible?
8259888
Simple random sampling uses a sample of size n from a population of size N to obtain data that can be used to make inferences about the characteristics of a population. Suppose that, from a population of 75 bank accounts, we want to take a random sample of ten accounts in order to learn about the population. How many different random samples of ten accounts are possible?
828931106354.9998
The prior probabilities for events A1 and A2 are P(A1) = .30 and P(A2) = .70. It is also known that P(A1 A2) = 0. Suppose P(B | A1) = .20 and P(B | A2) = .03.
Are events A1 and A2 mutually exclusive? Compute P(A1 B) (to 4 decimals). 0.06 Compute P(A2 B) (to 4 decimals). 0.021 Compute P(B) (to 4 decimals). 0.081 Apply Bayes' theorem to compute P(A1 | B) (to 4 decimals). 0.7407 Also apply Bayes' theorem to compute P(A2 | B) (to 4 decimals). 0.2593
The prior probabilities for events A1 and A2 are P(A1) = .40 and P(A2) = .60. It is also known that P(A1 A2) = 0. Suppose P(B | A1) = .20 and P(B | A2) = .05.
Are events A1 and A2 mutually exclusive? Compute P(A1 B) (to 4 decimals). 0.08 Compute P(A2 B) (to 4 decimals). 0.03 Compute P(B) (to 4 decimals). 0.11 Apply Bayes' theorem to compute P(A1 | B) (to 4 decimals). 0.7273 Also apply Bayes' theorem to compute P(A2 | B) (to 4 decimals). 0.2727
Scores turned in by an amateur golfer at the Bonita Fairways Golf Course in Bonita Springs, Florida, during 2005 and 2006 are as follows: 2005 Season 73 77 78 76 74 72 74 76 2006 Season 70 69 74 76 84 79 70 78
Calculate the mean (0 decimals) and the standard deviation (to 2 decimals) of the golfer's scores, for both years. 2005 Mean 75 Standard deviation 2.07 2006 Mean 75 Standard deviation 5.26 What is the primary difference in performance between 2005 and 2006? What improvement, if any, can be seen in the 2006 scores?
Scores turned in by an amateur golfer at the Bonita Fairways Golf Course in Bonita Springs, Florida, during 2005 and 2006 are as follows: 2005 Season 76 80 81 79 77 75 77 79 2006 Season 73 72 77 79 87 82 73 81
Calculate the mean (0 decimals) and the standard deviation (to 2 decimals) of the golfer's scores, for both years. 2005 Mean 78 Standard deviation 2.07 2006 Mean 78 Standard deviation 5.26 What is the primary difference in performance between 2005 and 2006? Variation in scores was higher in 2006 What improvement, if any, can be seen in the 2006 scores? in 2006 three of eight scores were
Scores turned in by an amateur golfer at the Bonita Fairways Golf Course in Bonita Springs, Florida, during 2011 and 2012 are as follows: 2011 Season 76 80 81 79 77 75 77 79 2012 Season 73 72 77 79 87 82 73 81
Calculate the mean (to the nearest whole number) and the standard deviation (to 2 decimals) of the golfer's scores, for both years. 2011 Mean 78 Standard deviation 2.07 2012 Mean 78 Standard deviation 5.26 What is the primary difference in performance between 2011 and 2012? Variation in scores was higher in 2012 What improvement, if any, can be seen in the 2012 scores? three of eight scores were lower
When a new machine is functioning properly, only 9% of the items produced are defective. Assume that we will randomly select two parts produced on the machine and that we are interested in the number of defective parts found.
Choose the Correct option from the above tree diagrams: b. How many experimental outcomes result in exactly one defect being found? 2 c. Compute the probabilities associated with finding no defects, exactly one defect, and two defects (to 4 decimals). P (no defects) 0.8281 P (1 defect) 0.1638 P (2 defects) 0.0081
When a new machine is functioning properly, only 4% of the items produced are defective. Assume that we will randomly select two parts produced on the machine and that we are interested in the number of defective parts found.
Choose the Correct option from the above tree diagrams: 2 b. How many experimental outcomes result in exactly one defect being found? 2 c. Compute the probabilities associated with finding no defects, exactly one defect, and two defects (to 4 decimals). P (no defects) .9409 P (1 defect) .0582 P (2 defects) .0009
In automobile mileage and gasoline-consumption testing, 13 automobiles were road tested for 300 miles in both city and highway driving conditions. The following data were recorded for miles-per-gallon performance. City: 18.2 18.7 17.9 16.4 15.2 17.3 18.8 18 18.1 17.3 17.2 17.3 18.2 Highway: 21.5 22.7 20.4 20.7 21.3 19.5 19.3 20.7 21.1 23.2 21.5 20.6 20.8 Calculate the mean, median, and mode for City and Highway gasoline consumption (to 1 decimal).
City Highway Mean 17.6 21.0 Median 17.9 20.8 Mode 17.3
In automobile mileage and gasoline-consumption testing, 13 automobiles were road tested for 300 miles in both city and highway driving conditions. The following data were recorded for miles-per-gallon performance. City: 18.8 19.3 18.5 17 15.8 17.9 19.4 18.6 18.7 17.9 17.8 17.9 18.8 Highway: 22.1 23.3 21 21.3 21.9 20.1 19.9 21.3 21.7 23.8 22.1 21.2 21.4 Calculate the mean, median, and mode for City and Highway gasoline consumption (to 1 decimal).
City Highway Mean 18.1 21.6 Median 18.2 21.4 Mode 17.9 Make a statement about the difference in gasoline consumption between both driving conditions.
In automobile mileage and gasoline-consumption testing, 13 automobiles were road tested for 300 miles in both city and highway driving conditions. The following data were recorded for miles-per-gallon performance. City: 18.8 19.3 18.5 17 15.8 17.9 19.4 18.6 18.7 17.9 17.8 17.9 18.8 Highway: 22.1 23.3 21 21.3 21.9 20.1 19.9 21.3 21.7 23.8 22.1 21.2 21.4 Calculate the mean, median, and mode for City and Highway gasoline consumption (to 1 decimal).
City Highway Mean 18.2 21.6 Median 18.5 21.4 Mode 17.9 Make a statement about the difference in gasoline consumption between both driving conditions.
Consider the following frequency distribution.
Class Frequency 40- 49 11 50- 59 13 60- 69 17 70- 79 7 80- 89 2 Construct a cumulative frequency distribution and a cumulative relative frequency distribution. Round your answers to two decimal places, if necessary. Class Cumulative Frequency Cumulative Relative Frequency less than or equal to 49 11 0.22 less than or equal to 59 24 0.48 less than or equal to 69 41 0.82 less than or equal to 79 48 0.96 less than or equal to 89 50 1
The response to a question has three alternatives: A, B, and C. A sample of 120 responses provides 52 A, 29 B, and 39 C. Show the frequency and relative frequency distributions (use nearest whole number for the frequency column and 2 decimal for the relative frequency column).
Class Frequency Relative Frequency A 52 0.43 B 29 0.24 C 39 0.33 (Total) 120 1.00
The response to a question has three alternatives: A, B, and C. A sample of 120 responses provides 59 A, 24 B, and 37 C. Show the frequency and relative frequency distributions (use nearest whole number for the frequency column and 2 decimal for the relative frequency column).
Class Frequency Relative Frequency A 59 0.49 B 24 0.20 C 37 0.31 (Total) 120 1.00
Airline passengers arrive randomly and independently at the passenger-screening facility at a major international airport. The mean arrival rate is 10 passengers per minute.
Compute the probability of no arrivals in a one-minute period (to 6 decimals). 0.000045 Compute the probability that three or fewer passengers arrive in a one-minute period (to 4 decimals). 0.0103 Compute the probability of no arrivals in a 15-second period (to 4 decimals). 0.0821 Compute the probability of at least one arrival in a 15-second period (to 4 decimals). 0.9179
Airline passengers arrive randomly and independently at the passenger-screening facility at a major international airport. The mean arrival rate is 8 passengers per minute.
Compute the probability of no arrivals in a one-minute period (to 6 decimals). 0.000335 Compute the probability that three or fewer passengers arrive in a one-minute period (to 4 decimals). 0.0424 Compute the probability of no arrivals in a 15-second period (to 4 decimals). 0.1353 Compute the probability of at least one arrival in a 15-second period (to 4 decimals). 0.8647
Correct Response eBook Video {Exercise 5.25 (Algorithmic)} Consider a binomial experiment with two trials and p =0.5. Which of the following tree diagrams accurately represents this binomial experiment?
Compute the probability of one success, f(1) (to 2 decimals). 0.5 Compute f(0) (to 2 decimals). 0.25 Compute f(2) (to 2 decimals). 0.25 Compute the probability of at least one success (to 2 decimals). 0.75 Compute the following (to 2 decimals). Expected value 1 Variance 0.5 Standard deviation 0.71
A university found that 40% of its students withdraw without completing the introductory statistics course. Assume that 20 students registered for the course.
Compute the probability that 2 or fewer will withdraw (to 4 decimals). .0036 Compute the probability that exactly 4 will withdraw (to 4 decimals). .0350 Compute the probability that more than 3 will withdraw (to 4 decimals). .9840 Compute the expected number of withdrawals. 8
A university found that 30% of its students withdraw without completing the introductory statistics course. Assume that 20 students registered for the course.
Compute the probability that 2 or fewer will withdraw (to 4 decimals). 0.0355 Compute the probability that exactly 4 will withdraw (to 4 decimals). 0.1304 Compute the probability that more than 3 will withdraw (to 4 decimals). 0.8929 Compute the expected number of withdrawals. 6
The following frequency distribution shows the price per share for a sample of 30 companies listed on the New York Stock Exchange. Price per Share Frequency $20-29 6 $30-39 6 $40-49 6 $50-59 3 $60-69 2 $70-79 2 $80-89 5
Compute the sample mean price per share and the sample standard deviation of the price per share for the New York Stock Exchange companies (to 2 decimals). Assume there are no price per shares between 29 and 30, 39 and 40, etc. Sample mean $ 49.50 Sample standard deviation $ 21.29
Consider a sample with data values of 26, 25, 20, 17, 31, 34, 28, and 25. Compute the range, interquartile range, variance, and standard deviation (to a maximum of 2 decimals, if decimals are necessary).
Consider a sample with data values of 26, 25, 20, 17, 31, 34, 28, and 25. Compute the range, interquartile range, variance, and standard deviation (to a maximum of 2 decimals, if decimals are necessary). Range 17 Interquartile range 9 Variance 30.21 Standard deviation 5.5
Consider a sample with a mean of 30 and a standard deviation of 4. Use Chebyshev's theorem to determine the percentage of the data within each of the following ranges (to the nearest whole number).
Correct Response eBook Video {Extra Exercise #2 (Algorithmic)} Consider a sample with a mean of 30 and a standard deviation of 4. Use Chebyshev's theorem to determine the percentage of the data within each of the following ranges (to the nearest whole number). 10 to 50, at least 96 % 5 to 55, at least 97 % 21 to 39, at least 80 % 17 to 43, at least 91 % 14 to 46, at least 94 %
The following data are for 30 observations involving two categorical variables, x and y. The categories for x are A, B, and C; the categories for y are 1 and 2.
Develop a crosstabulation for the data, with x as the row variable and y as the column variable. y 1 2 Total A 5 0 5 x B 2 11 13 C 10 2 12 Total 17 13 30 Compute the row percentages (to 1 decimal). y 1 2 Total A 100.0 % 0.0 % 100.0 % x B 15.4 % 84.6 % 100.0 % C 83.3 % 16.7 % 100.0 % Compute the column percentages (to 1 decimal). y 1 2 A 29.4 % 0.0 % x B 11.8 % 84.6 % C 58.8 % 15.4 % Total 100.0 % 100.0 % Describe the observed relationship between variables x and y. Category A values for x are associated with category 1 values for y. always Category B values for x are associated with category 1 values for y. not usually Category C values for x are associated with category 2 values for y. not usually
Students taking the Graduate Management Admissions Test (GMAT) were asked about their undergraduate major and intent to pursue their MBA as a full-time or part-time student. A summary of their responses follows.
Develop a joint probability table for these data (to 3 decimals). Undergraduate Major Business Engineering Other Totals Intended Enrollment Full-Time .218 .204 .040 .462 Status Part-Time .208 .306 .024 .538 Totals .426 .510 .064 1.00 Use the marginal probabilities of undergraduate major (Business, Engineering, or Other) to comment on which undergraduate major produces the most potential MBA students. If a student intends to attend classes full-time in pursuit of an MBA degree, what is the probability that the student was an undergraduate Engineering major (to 3 decimals)? .442 If a student was an undergraduate Business major, what is the probability that the student intends to attend classes full-time in pursuit of an MBA degree (to 3 decimals)? .512 Let A denote the event that student intends to attend classes full-time in pursuit of an MBA degree, and let B denote the event that the student was an undergraduate Business major. Are events A and B independent? Hide Feedback Correct Solution Correct Response eBook Video {Exercise 4.33 (Algorithmic)} Students taking the Graduate Management Admissions Test (GMAT) were asked about their undergraduate major and intent to pursue their MBA as a full-time or part-time student. A summary of their responses follows. Undergraduate Major Business Engineering Other Totals Intended Enrollment Full Time 421 394 77 892 Status Part Time 402 590 46 1,038 Totals 823 984 123 1,930 Develop a joint probability table for these data (to 3 decimals). Undergraduate Major Business Engineering Other Totals Intended Enrollment Full-Time 0.218 0.204 0.040 0.462 Status Part-Time 0.208 0.306 0.024 0.538 Totals 0.426 0.510 0.064 1.00 Use the marginal probabilities of undergraduate major (Business, Engineering, or Other) to comment on which undergraduate major produces the most potential MBA students. If a student intends to attend classes full-time in pursuit of an MBA degree, what is the probability that the student was an undergraduate Engineering major (to 3 decimals)? 0.442 If a student was an undergraduate Business major, what is the probability that the student intends to attend classes full-time in pursuit of an MBA degree (to 3 decimals)? 0.512 Let A denote the event that student intends to attend classes full-time in pursuit of an MBA degree, and let B denote the event that the student was an undergraduate Business major. Are events A and B independent?
A doctor's office staff studied the waiting times for patients who arrive at the office with a request for emergency service. The following data with waiting times in minutes were collected over a one-month period. 5 5 10 17 4 4 2 19 12 6 9 7 16 21 7 7 6 14 18 2
Fill in the frequency (to the nearest whole number) and the relative frequency (2 decimals) values below. Waiting Time Frequency Relative Frequency 0-4 4 0.2 5-9 8 0.4 10-14 3 0.15 15-19 4 0.2 20-24 1 0.05 (Total) 20 1.00 Fill in the cumulative frequency (to the nearest whole number) and the cumulative relative frequency (2 decimals) values below. Waiting Time Cumulative Frequency Cumulative Relative Frequency Less than or equal to 4 4 0.2 Less than or equal to 9 12 0.6 Less than or equal to 14 15 0.75 Less than or equal to 19 19 0.95 Less than or equal to 24 20 1.00 What proportion of patients needing emergency service wait 19 minutes or less? 0.95
Suppose that we have a sample space S = {E1, E2, E3, E4, E5, E6, E7}, where E1, E2, ..., E7 denote the sample points. The following probability assignments apply: P(E1) = 0.1, P(E2) = 0.15, P(E3) = 0.1, P(E4) = 0.2, P(E5) = 0.15, P(E6) = 0.05, and P(E7) = 0.25.
Find P(A), P(B), and P(C). P(A) 0.35 P(B) 0.6 P(C) 0.65 What is P(A B)? 0.75 What is P(A B)? 0.2 Are events A and C mutually exclusive? What is P(Bc )? 0.4
The National Sporting Goods Association conducted a survey of persons 7 years of age or older about participation in sports activities (Statistical Abstract of the United States: 2002). The total population in this age group was reported at 248.5 million, with 120.9 million male and 127.6 million female. The number of participants for the top five sports activities appears here.
For a randomly selected female, estimate the probability of participation in each of the sports activities (to 2 decimals). Note that the probabilities do not sum to 1 because of participation in more than one sports activity. Bicycle riding 0.15 Camping 0.18 Exercise walking 0.44 Exercising with equipment 0.18 Swimming 0.26 For a randomly selected male, estimate the probability of participation in each of the sports activities (to 2 decimals). Note that the probabilities do not sum to 1 because of participation in more than one sports activity. Bicycle riding 0.17 Camping 0.22 Exercise walking 0.25 Exercising with equipment 0.16 Swimming 0.21 For a randomly selected person, what is the probability the person participates in exercise walking (to 2 decimals)? 0.35 Suppose you just happen to see an exercise walker going by. What is the probability the walker is a woman (to 2 decimals)? 0.65 What is the probability the walker is a man (to 2 decimals)? 0.35
Consider the experiment of tossing a coin three times.
How many experimental outcomes exist? 8 Let x denote the number of heads occurring on three coin tosses. Show the value the random variable would have for each of the experimental outcomes. Outcome Value of x (Tail, Tail, Head) 1 (Head, Tail, Tail) 1 (Head, Tail, Head) 2 (Tail, Tail, Tail) 0 (Tail, Head, Tail) 1 (Head, Head, Tail) 2 (Head, Head, Head) 3 (Tail, Head, Head) 2 Is this random variable discrete or continuous? It is discrete
Consider the experiment of tossing a coin three times.
How many experimental outcomes exist? 8 Let x denote the number of heads occurring on three coin tosses. Show the value the random variable would have for each of the experimental outcomes. Outcome Value of x (Tail, Head, Tail) 1 (Head, Tail, Head) 2 (Tail, Head, Head) 2 (Head, Tail, Tail) 1 (Head, Head, Head) 3 (Tail, Tail, Head) 1 (Head, Head, Tail) 2 (Tail, Tail, Tail) 0 Is this random variable discrete or continuous? discrete
Consider the random experiment of selecting a playing card from a deck of 52 playing cards. Each card corresponds to a sample point with a 1/52 probability.
How many sample points are there in the event that a jack is selected? 4 How many sample points are there in the event that a diamond is selected? 13 How many sample points are there in the event that a non face card (non jack, non queen, or non king) is selected? 40 Find the probabilities associated with each of the events in parts (a), (b), and (c) (to 2 decimals). (a) Ace .08 (b) Club .25 (c) Non face card 0.77
Consider the random experiment of selecting a playing card from a deck of 52 playing cards. Each card corresponds to a sample point with a 1/52 probability.
How many sample points are there in the event that an ace is selected? 4 How many sample points are there in the event that a spade is selected? 13 How many sample points are there in the event that a face card ( jack, queen, or king) is selected? 12 Find the probabilities associated with each of the events in parts (a), (b), and (c) (to 2 decimals). (a) Ace .08 (b) Club .25 (c) Face card 0.23
Assume that we have two events, A and B, that are mutually exclusive. Assume further that we know P(A) = 0.65 and P(B) = 0.35.
If an amount is zero, enter "0". What is P(A B)? 0 What is P(A | B)? 0 Is P(A | B) equal to P(A)? No Are events A and B dependent or independent? Dependent A student in statistics argues that the concepts of mutually exclusive events and independent events are really the same, and that if events are mutually exclusive they must be independent. Is this statement accurate? No What general conclusion would you make about mutually exclusive and independent events given the results of this problem? Mutually exclusive events are dependent
In San Francisco, 30% of workers take public transportation daily (USA Today, December 21, 2005).
In a sample of 6 workers, what is the probability that exactly three workers take public transportation daily (to 4 decimals including interim calculations)? 0.1852 In a sample of 6 workers, what is the probability that at least three workers take public transportation daily (to 4 decimals including interim calculations)? 0.2557
A questionnaire provides 54 Yes, 33 No, and 33 no-opinion answers.
In the construction of a pie chart, how many degrees would be in the section of the pie showing the Yes answers? 162 degrees How many degrees would be in the section of the pie showing the No answers? 99 degrees If you constructed a pie chart, what percentage of the circle that would be occupied by each response. Round answers to one decimal place. Yes 45 % No 27.5 % No Opinion 27.5 %
The number of students taking the SAT has risen to an all-time high of more than 1.5 million (College Board, August 26, 2008). Students are allowed to repeat the test in hopes of improving the score that is sent to college and university admission offices. The number of times the SAT was taken and the number of students are as follows.
Number of Times Number of Students 1 752,000 2 609,000 3 121,000 4 30,000 5 8,900 a. Let x be a random variable indicating the number of times a student takes the SAT. Show the probability distribution for this random variable. Round your answers to four decimal places. x f(x) 1 0.4944 2 0.4004 3 0.0796 4 0.0197 5 0.0059 b. What is the probability that a student takes the SAT more than one time? Round your answer to four decimal places. 0.5056 c. What is the probability that a student takes the SAT three or more times? Round your answer to four decimal places. 0.1052 d. What is the expected value of the number of times the SAT is taken? Round your interim calculations and final answer to four decimal places. 1.6421 What is your interpretation of the expected value? The input in the box below will not be graded, but may be reviewed and considered by your instructor. * e. What is the variance and standard deviation for the number of times the SAT is taken? Round your interim calculations and final answer to four decimal places. Variance 0.5779 Standard deviation 0.7602
Annual sales, in millions of dollars, for 21 pharmaceutical companies follow. 8,660 1,415 1,928 9,145 2,533 11,755 626 14,138 6,646 1,906 2,903 1,397 10,813 7,702 4,140 4,471 761 2,191 3,763 5,968 8,554
Provide a five-number summary. If needed, round your answer to a whole number. Smallest value 626 First quartile 1928 Median 4140 Third quartile 8554 Largest value 14138 Compute the lower and upper limits. Enter negative amounts with a minus sign. Lower limit -8011 Upper limit 18493 Do the data contain any outliers? No Johnson & Johnson's sales are the largest on the list at $14,138 million. Suppose a data entry error (a transposition) had been made and the sales had been entered as $41,138 million. Would the method of detecting outliers in part (c) identify this problem and allow for correction of the data entry error? yes a transposition would have detected an outlier
Consider a sample with data values of 26, 24, 20, 17, 32, 35, 28, and 24. Compute the range, interquartile range, variance, and standard deviation (to a maximum of 2 decimals, if decimals are necessary).
Range 18 Interquartile range 10 Variance 35.07 Standard deviation 5.92
Consider a sample with data values of 26, 24, 22, 16, 32, 35, 28, and 24. Compute the range, interquartile range, variance, and standard deviation (to a maximum of 2 decimals, if decimals are necessary. Use Excel's =quartile.exc function).
Range 19 Interquartile range 8.5 Variance 34.98 Standard deviation 5.91
A bowler's scores for six games were 183, 166, 189, 196, 173, and 177. Using these data as a sample, compute the following descriptive statistics:
Range 30 b. Variance (to 1 decimal) 119.5 c. Standard deviation (to 2 decimals) 10.93 d. Coefficient of variation (to 2 decimals) 6.05 %
The National Highway Traffic Safety Administration (NHTSA) conducted a survey to learn about how drivers throughout the United States are using seat belts (Associated Press, August 25, 2003). Sample data consistent with the NHTSA survey are as follows. Driver Using Seat Belt?
Region Yes No Northeast 148 55 Midwest 164 54 South 271 71 West 254 45 Total 837 225 Combining the results from all four regions, what is the probability that a U.S. driver is using a seat belt (to 2 decimals)? 0.79 The seat belt usage probability for a U.S. driver a year earlier was .75. NHTSA chief Dr. Jeffrey Runge had hoped for a .78 probability in 2003. Would he have been pleased with the 2003 survey results? yes bc his expectations were exceeded What is the probability of seat belt usage by region of the country (to 2 decimals)? Northeast 0.73 Midwest 0.75 South 0.79 West 0.85 What region has the highest probability of seat belt usage? (to 2 decimals) west
In an article about investment alternatives, Money magazine reported that drug stocks provide a potential for long-term growth, with over 55% of the adult population of the United States taking prescription drugs on a regular basis. For adults age 65 and older, 85% take prescription drugs regularly. For adults age 18 to 64, 47% take prescription drugs regularly. The age 18-64 age group accounts for 86.3% of the adult population (Statistical Abstract of the United States, 2008).
Round your answers to 4 decimal places. a. What is the probability that a randomly selected adult is 65 or older? 0.137 b. Given an adult takes prescription drugs regularly, what is the probability that the adult is 65 or older? 0.2231
In an article about investment alternatives, Money magazine reported that drug stocks provide a potential for long-term growth, with over 54% of the adult population of the United States taking prescription drugs on a regular basis. For adults age 65 and older, 83% take prescription drugs regularly. For adults age 18 to 64, 46% take prescription drugs regularly. The age 18-64 age group accounts for 84% of the adult population (Statistical Abstract of the United States, 2008).
Round your answers to 4 decimal places. a. What is the probability that a randomly selected adult is 65 or older? 0.16 b. Given an adult takes prescription drugs regularly, what is the probability that the adult is 65 or older? 0.2558
Correct Response eBook {Exercise 5.55 (Algorithmic)} The budgeting process for a midwestern college resulted in expense forecasts for the coming year (in $ millions) of $9, $10, $11, $12, and $13. Because the actual expenses are unknown, the following respective probabilities are assigned: 0.25, 0.18, 0.22, 0.17, and 0.18.
Show the probability distribution for the expense forecast. x f(x) 9 0.25 10 0.18 11 0.22 12 0.17 13 0.18 What is the expected value of the expense forecast for the coming year (to 2 decimals)? 10.85 What is the variance of the expense forecast for the coming year (to 2 decimals)? 2.05 If income projections for the year are estimated at $12 million, how much profit does the college expect to make (report your answer in millions of dollars, to 2 decimals)? 1.15
The budgeting process for a midwestern college resulted in expense forecasts for the coming year (in $ millions) of $9, $10, $11, $12, and $13. Because the actual expenses are unknown, the following respective probabilities are assigned: 0.26, 0.15, 0.21, 0.18, and 0.2.
Show the probability distribution for the expense forecast. x f(x) 9 0.26 10 0.15 11 0.21 12 0.18 13 0.2 What is the expected value of the expense forecast for the coming year (to 2 decimals)? 10.91 What is the variance of the expense forecast for the coming year (to 2 decimals)? 2.16 If income projections for the year are estimated at $12 million, how much profit does the college expect to make (report your answer in millions of dollars, to 2 decimals)? 1.09
The budgeting process for a midwestern college resulted in expense forecasts for the coming year (in $ millions) of $9, $10, $11, $12, and $13. Because the actual expenses are unknown, the following respective probabilities are assigned: 0.26, 0.16, 0.21, 0.16, and 0.21.
Show the probability distribution for the expense forecast. x f(x) 9 0.26 10 0.16 11 0.21 12 0.16 13 0.21 What is the expected value of the expense forecast for the coming year (to 2 decimals)? 10.9 What is the variance of the expense forecast for the coming year (to 2 decimals)? 2.19 If income projections for the year are estimated at $12 million, how much profit does the college expect to make (report your answer in millions of dollars, to 2 decimals)? 1.1
Refer to the KP&L sample points and sample point probabilities in Tables 4.2 and 4.3.
The design stage (stage 1) will run over budget if it takes 4 months to complete. List the sample points in the event the design stage is over budget. What is the probability that the design stage is over budget (to 2 decimal)? 0.45 The construction stage (stage 2) will run over budget if it takes 9 months to complete. List the sample points in the event the construction stage is over budget. What is the probability that the construction stage is over budget (to 2 decimals)? 0.35 What is the probability that both stages are over budget (to 2 decimals)? 0.25
The following data were collected by counting the number of operating rooms in use at Tampa General Hospital over a 20-day period: On four of the days only one operating room was used, on six of the days two were used, on eight of the days three were used, and on two days all four of the hospital's operating rooms were used. Round your answers to two decimal places.
The following data were collected by counting the number of operating rooms in use at Tampa General Hospital over a 20-day period: On four of the days only one operating room was used, on six of the days two were used, on eight of the days three were used, and on two days all four of the hospital's operating rooms were used. Round your answers to two decimal places. a. Use the relative frequency approach to construct an empirical discrete probability distribution for the number of operating rooms in use on any given day. x f(x) 1 0.2 2 0.3 3 0.4 4 0.1 Total 1.00 Choose the correct graph from the above Graphs: c. Show that your probability distribution satisfies the required conditions for a valid discrete probability distribution. 3 Because f(x) 0 for x = 1, 2, 3, 4 and sum f(1) + f(2) + f(3) + f(4) = 1. >_
The Canmark Research Center Airport Customer Satisfaction Survey uses an online questionnaire to provide airlines and airports with customer satisfaction ratings for all aspects of the customers' flight experience. After completing a flight, customers receive an email asking them to go to the website and rate a variety of factors, including the reservation process, the check-in process, luggage policy, cleanliness of gate area, service by flight attendants, food/beverage selection, on-time arrival, and so on. A five-point scale, with Excellent (E), Very Good (V), Good (G), Fair (F), and Poor (P), is used to record the customer ratings for each survey question. Assume that passengers on a Delta Airlines flight from Myrtle Beach, South Carolina, to Atlanta, Georgia, provided the following ratings for the question, "Please rate the airline based on your overall experience with this flight." The sample ratings are shown below.
To summarize the above data. Rating Frequency Percent Frequency Excellent 17 34 Very Good 26 52 Good 4 8 Fair 1 2 Poor 2 4 Total 50 100 What do these summaries indicate about the overall customer satisfaction with the Delta flight? 94 % of customers are satisfied with the Delta flight at either a good, very good, or excellent rating. Only 6 % of customers rated the Delta flight Fair or Poor. b. The online survey questionnaire enabled respondents to explain any aspect of the flight that failed to meet expectations. Would this be helpful information to a manager looking for ways to improve the overall customer satisfaction on Delta flights? Explain. Allowing survey respondents to explain their 5-point scale responses would provide helpful information to managers looking for ways to improve customer satisfaction on Delta flights. The 4 % respondents indicating that the flight failed to meet expectations would have the opportunity to provide detailed information about their expectations.
Many students accumulate debt by the time they graduate from college. Shown in the following table is the percentage of graduates with debt and the average amount of debt for these graduates at four universities and four liberal arts colleges.
University % with Debt Amount($) College % with Debt Amount($) 1 79 32,930 1 83 28,759 2 66 32,110 2 96 24,000 3 53 11,221 3 53 10,209 4 61 11,856 4 46 11,016 a. If you randomly choose a graduate of College 2, what is the probability that this individual graduated with debt (to 2 decimals)? 0.96 b. If you randomly choose one of these eight institutions for a follow-up study on student loans, what is the probability that you will choose an institution with more than 90% of its graduates having debt (to 3 decimals)? 0.125 c. If you randomly choose one of these eight institutions for a follow-up study on student loans, what is the probability that you will choose an institution whose graduates with debts have an average debt of more than $ 22,000 (to 3 decimals)? 0.5 d. What is the probability that a graduate of University 1 does not have debt (to 2 decimals)? 0.21 e. For graduates of University 1 with debt, the average amount of debt is $ 32,930. Considering all graduates from University 1, what is the average debt per graduate? Round to nearest dollar. $ 26015
The results of a national survey showed that on average, adults sleep 6.9 hours per night. Suppose that the standard deviation is 1.4 hours. Round your answers to the nearest whole number.
Use Chebyshev's theorem to calculate the percentage of individuals who sleep between 4.1 and 9.7 hours. At least 75 % Use Chebyshev's theorem to calculate the percentage of individuals who sleep between 3.9 and 9.9 hours. At least 78 % Assume that the number of hours of sleep follows a bell-shaped distribution. Use the empirical rule to calculate the percentage of individuals who sleep between 4.1 and 9.7 hours per day. 95 % How does this result compare to the value that you obtained using Chebyshev's theorem in part (a)? the empirical rule produces a larger percentage than chebcevs therom
The results of a national survey showed that on average, adults sleep 6.9 hours per night. Suppose that the standard deviation is 1.2 hours. Round your answers to the nearest whole number.
Use Chebyshev's theorem to calculate the percentage of individuals who sleep between 4.5 and 9.3 hours. At least 75 % Use Chebyshev's theorem to calculate the percentage of individuals who sleep between 3.9 and 9.9 hours. At least 84 % Assume that the number of hours of sleep follows a bell-shaped distribution. Use the empirical rule to calculate the percentage of individuals who sleep between 4.5 and 9.3 hours per day. 95 % How does this result compare to the value that you obtained using Chebyshev's theorem in part (a)? empirical rule produces a larger percentatge
The following data were collected by counting the number of operating rooms in use at Tampa General Hospital over a 20-day period: On four of the days only one operating room was used, on six of the days two were used, on eight of the days three were used, and on two days all four of the hospital's operating rooms were used. Round your answers to two decimal places.
Use the relative frequency approach to construct an empirical discrete probability distribution for the number of operating rooms in use on any given day. x f(x) 1 0.2 2 0.3 3 0.4 4 0.1 Total 1.00 Choose the correct graph from the above Graphs: c. Show that your probability distribution satisfies the required conditions for a valid discrete probability distribution. Because f(x) 0 for x = 1, 2, 3, 4 and sum f(1) + f(2) + f(3) + f(4) = 1.
A doctor's office staff studied the waiting times for patients who arrive at the office with a request for emergency service. The following data with waiting times in minutes were collected over a one-month period. 2 5 10 13 3 2 3 17 12 8 9 7 15 22 8 9 9 13 17 5 Fill in the frequency (to the nearest whole number) and the relative frequency (2 decimals) values below.
Waiting Time Frequency Relative Frequency 0-4 4 0.2 5-9 8 0.4 10-14 4 0.2 15-19 3 0.15 20-24 1 0.05 (Total) 20 1.00 Fill in the cumulative frequency (to the nearest whole number) and the cumulative relative frequency (2 decimals) values below. Waiting Time Cumulative Frequency Cumulative Relative Frequency Less than or equal to 4 4 0.2 Less than or equal to 9 12 0.6 Less than or equal to 14 16 0.8 Less than or equal to 19 19 0.95 Less than or equal to 24 20 1.00 What proportion of patients needing emergency service wait 14 minutes or less? 0.8
Five observations taken for two variables follow. xi 3 5 12 4 15 yi 50 40 30 50 20 Which of the following scatter diagrams accurately represents the data set?
What does the scatter diagram developed in part (a) indicate about the relationship between the two variables? Compute the sample covariance. -68 Compute the sample correlation coefficient (to 3 decimals). -0.974 What can you conclude, based on your computation of the sample correlation coefficient? There is a strong negative linear relatiosnip
Five observations taken for two variables follow. xi 4 5 10 5 15 yi 50 40 30 50 20
What does the scatter diagram developed in part (a) indicate about the relationship between the two variables? The relationship is negative Compute the sample covariance. -58 Compute the sample correlation coefficient (to 3 decimals). -0.955 What can you conclude, based on your computation of the sample correlation coefficient? Strong negative linear relationship
Assume that we have two events, A and B, that are mutually exclusive. Assume further that we know P(A) = 0.65 and P(B) = 0.35. If an amount is zero, enter "0".
What is P(A B)? 0 What is P(A | B)? 0 Is P(A | B) equal to P(A)? No Are events A and B dependent or independent? Dependednt A student in statistics argues that the concepts of mutually exclusive events and independent events are really the same, and that if events are mutually exclusive they must be independent. Is this statement accurate? no What general conclusion would you make about mutually exclusive and independent events given the results of this problem? Mutually exclusive events are dependent
A consulting firm submitted a bid for a large research project. The firm's management initially felt they had a 50-50 chance of getting the project. However, the agency to which the bid was submitted subsequently requested additional information on the bid. Past experience indicates that for 77% of the successful bids and 35% of the unsuccessful bids the agency requested additional information.
What is the prior probability of the bid being successful (that is, prior to the request for additional information) (to 1 decimal)? 0.5 What is the conditional probability of a request for additional information given that the bid will ultimately be successful (to 2 decimals)? 0.77 Compute the posterior probability that the bid will be successful given a request for additional information (to 2 decimals). 0.69
A consulting firm submitted a bid for a large research project. The firm's management initially felt they had a 50-50 chance of getting the project. However, the agency to which the bid was submitted subsequently requested additional information on the bid. Past experience indicates that for 80% of the successful bids and 37% of the unsuccessful bids the agency requested additional information.
What is the prior probability of the bid being successful (that is, prior to the request for additional information) (to 1 decimal)? 0.5 What is the conditional probability of a request for additional information given that the bid will ultimately be successful (to 2 decimals)? 0.8 Compute the posterior probability that the bid will be successful given a request for additional information (to 2 decimals). 0.68
A company studied the number of lost-time accidents occurring at its Brownsville, Texas, plant. Historical records show that 8% of the employees suffered lost-time accidents last year. Management believes that a special safety program will reduce such accidents to 6% during the current year. In addition, it estimates that 15% of employees who had lost-time accidents last year will experience a lost-time accident during the current year.
What is the probability an employee will experience a lost-time accident in both years (to 3 decimals)? .012 What is the probability an employee will experience a lost-time accident over the two-year period (to 3 decimals)? .128
Figure 1.11 provides a bar chart showing the amount of federal spending for the years 2004 to 2010 (Congressional Budget Office website, May 15, 2011).
What is the variable of interest? b. Are the data categorical or quantitative? Quantitative c. Are the data time series or cross-sectional? time series d. Comment on the trend in federal spending over time. Increased but only shown a decrese in 2010 How much did the federal government spend in 2007? $ 2.8 trillions (to 1 decimal)
Consider a Poisson distribution with a mean of two occurrences per time period.
Which of the following is the appropriate Poisson probability function for one time period? 1 2 3 What is the expected number of occurrences in three time periods? 6 Select the appropriate Poisson probability function to determine the probability of x occurrences in three time periods. 1 2 3 Compute the probability of two occurrences in three time periods (to 4 decimals). 0.0446 Compute the probability of five occurrences in one time period (to 4 decimals). 0.0361 Compute the probability of seven occurrences in two time periods (to 4 decimals). 0.0595
Consider a binomial experiment with two trials and p =0.8.
Which of the following tree diagrams accurately represents this binomial experiment? #1 Compute the probability of one success, f(1) (to 2 decimals). 0.32 Compute f(0) (to 2 decimals). 0.04 Compute f(2) (to 2 decimals). 0.64 Compute the probability of at least one success (to 2 decimals). 0.96 Compute the following (to 2 decimals). Expected value 1.6 Variance 0.32 Standard deviation 0.57
The following table provides a probability distribution for the random variable y. y f(y) 2 0. 10 5 0. 20 7 0. 40 8 0. 30
a. Compute E(y) (to 1 decimal). 6.4 b. Compute Var(y) and σ (to 2 decimals). Var(y) 3.24 σ 1.8
The grade point average for college students is based on a weighted mean computation. For most colleges, the grades are given the following data values: A (4), B (3), C (2), D (1), and F (0). After 60 credit hours of course work, a student at State University earned 9 credit hours of A, 15 credit hours of B, 31 credit hours of C, and 5 credit hours of D.
a. Compute the student's grade point average. Round your answer to two decimal places. 2.47 b. Students at State University must maintain a 2.5 grade point average for their first 60 credit hours of course work in order to be admitted to the business college. Will this student be admitted? no
The grade point average for college students is based on a weighted mean computation. For most colleges, the grades are given the following data values: A (4), B (3), C (2), D (1), and F (0). After 60 credit hours of course work, a student at State University earned 9 credit hours of A, 15 credit hours of B, 32 credit hours of C, and 4 credit hours of D.
a. Compute the student's grade point average. Round your answer to two decimal places. 2.48 b. Students at State University must maintain a 2.5 grade point average for their first 60 credit hours of course work in order to be admitted to the business college. Will this student be admitted?
Suppose that we have two events, A and B, with P(A) = .50, P(B) = .70, and P(A ∩ B) = .30.
a. Find P(A | B) (to 4 decimals). 0.4286 b. Find P(B | A) (to 4 decimals). 0.6 c. Are A and B independent? Why or why not? because P(A | B) P(A) no; not equal to
A local bank reviewed its credit card policy with the intention of recalling some of its credit cards. In the past approximately 6% of cardholders defaulted, leaving the bank unable to collect the outstanding balance. Hence, management established a prior probability of .06 that any particular cardholder will default. The bank also found that the probability of missing a monthly payment is .20 for customers who do not default. Of course, the probability of missing a monthly payment for those who default is 1.
a. Given that a customer missed one or more monthly payments, compute the posterior probability that the customer will default (to 2 decimals). 0.24 b. The bank would like to recall its card if the probability that a customer will default is greater than .20. Should the bank recall its card if the customer misses a monthly payment? Why or why not?
A local bank reviewed its credit card policy with the intention of recalling some of its credit cards. In the past approximately 8% of cardholders defaulted, leaving the bank unable to collect the outstanding balance. Hence, management established a prior probability of .08 that any particular cardholder will default. The bank also found that the probability of missing a monthly payment is .20 for customers who do not default. Of course, the probability of missing a monthly payment for those who default is 1.
a. Given that a customer missed one or more monthly payments, compute the posterior probability that the customer will default (to 2 decimals). 0.3 b. The bank would like to recall its card if the probability that a customer will default is greater than .20. Should the bank recall its card if the customer misses a monthly payment? Why or why not? yes the probability of default is greater than 20
A bowler's scores for six games were 181, 162, 187, 191, 172, and 177. Using these data as a sample, compute the following descriptive statistics:
a. Range 29 b. Variance (to 1 decimal) 110.3 c. Standard deviation (to 2 decimals) 10.5 d. Coefficient of variation (to 2 decimals) 5.89 %
A survey of magazine subscribers showed that 45.9% rented a car during the past 12 months for business reasons, 55% rented a car during the past 12 months for personal reasons, and 20% rented a car during the past 12 months for both business and personal reasons.
a. What is the probability that a subscriber rented a car during the past 12 months for business or personal reasons? 0.809 b. What is the probability that a subscriber did not rent a car during the past 12 months for either business or personal reasons? 0.191