Econ Quizs/Homework Answers
For a normally distributed population with a mean of 225 and standard deviation of 40, approximately what percentage of the observations should we expect to lie between 185 and 265?
68.0 % observations
A lamp manufacturer has developed five lamp bases and four lampshades that could be used together. How many different arrangements of base and shade can be offered?
20
What does 6!2!/4!3! equal?
10
A sample of 9 people was asked how many times they ate out at a restaurant so far this year. Results are: 1618132228136 3214 a.(2 points) Manually calculate the mean (show your actual formula and calculations even if using a programmable calculator). b.(1 point) What is the mode? c.(2 points) What is the range? d.(5 points) Manually calculate the standard deviation of the sample (show all calculations and formulas, even if using a programmable calculator). Answers without required work are worth zero value!
162/9 = 18 b)13 c)32 ‒ 6 = 26 d)s = =
Refer to the following frequency distribution on days absent during a calendar year by employees of a manufacturing company: Days Absent. Number of Employees 42 up to 47 65 47 up to 52 35 52 up to 57 11 57 up to 62 7 62 up to 67 2 How many employees were absent from 36 up to 46 days?
18
A popular smart phone has an average battery life of 8.0 hours on a single charge with a standard deviation of 1.1 hours. Assuming these battery life measures have a bell-shaped distribution, approximately what percent of phones will function for less than 5.8 hours on a single charge of the battery?
2.5 %
The numbers 0 through 9 are used in code groups of four to identify an item of clothing. Code 1083 might identify a blue blouse, size medium. The code group 2031 might identify a pair of pants, size 18, and so on. Repetitions of numbers are not permitted, i.e., the same number cannot be used more than once in a total sequence. As examples, 2256, 2562 or 5559 would not be permitted. How many different code groups can be designed?
5,040
Which one of the following best describes a frequency table?
A grouping of qualitative data into classes showing the number of observations in each class.
Statistics is a science that deals with which of the following with regard to data? Multiple Choice: Interpretation All of these Collection and organization Presentation and analysis
All of these
Statistics is a science that deals with the collection, organization, and ____________ of data. Multiple Choice: analysis interpretation presentation All of these.
All of these.
A ____________ organizes categorical data into an easy-to-read format the shows the number of observations in each class.
frequency table
Statistics is usually divided into which categories?
Descriptive and inferential
A group of employees of Unique Services will be surveyed about a new pension plan. In-depth interviews with each employee selected in the sample will be conducted. The employees are classified as follows: Class. Event number supervisor. A. 120 Maintenance. B. 50 Production. C. 1460 Management. D. 320 Secretarial E. 68 What is the probability that the first person selected is either in maintenance or in secretarial?
Given mutually exclusive classes, P(maintenance or secretarial) = P(maintenance) + P(secretarial) = 50/2000 + 68/2000 = 0.059. .059
Data can broadly be split into non-numeric and numeric data. Which of the following is (are) example(s) of how we can further split numeric data? (I) Qualitative (II) Discrete (III) Quantitative (IV) Continuous
II and IV
For a bell-shaped distribution with a mean of 250 and a standard deviation of 45, what interval should contain approximately 99.7% of the data?
Lower interval limit = 115. Upper interval limit = 385.
For a normally distributed population with a mean of 235 and a standard deviation of 35, what interval should contain approximately 68% of the data?
Lower interval limit = 200. Upper interval limit = 270.
Within a given population, 22% of the people are smokers, 57% of the people are males and 12% are both male and smoker. If a person is chosen at random from the population, what is the probability that the selected person is either a male or a smoker?
Use formula for union of two events: 0.22 + 0.57 - 0.12 = 0.67
a. A manager wants to assign seven sales representatives to seven customer accounts (one each). How many possible assignments exist? b. A librarian wants to arrange eight books on a bookshelf. How many possible arrangements (orderings) exist for these eight books? c. A production manager must schedule twelve jobs to run on a single machine (one job at a time). In how many possible sequences (orderings) can these twelve jobs be run?
hese questions all pertain to the Factorial Operation, since we are interested in how many possible outcomes exist for a series of steps (events) in which the number of possible options decreases by one at each step. a. 7! = 5,040 assignments. b. 8! = 40,320 arrangements. c. 12! = 479,001,600 sequences.
A sales manager for a credit card processing company needs to report the typical earnings for members of his sales team. The sales manager wants to summarize the earnings for the team using either the mean, median, or mode. If the top sales person earns dramatically more than anyone else on the team, which measure of the center would be the safest choice to represent the typical earnings for these sales people?
median
The ____________ is the middle value in a data set that has been arranged in order of decreasing or increasing size.
median
A real estate agent has received multiple offers on a beachfront condo in Deerfield Beach, Florida. Find the median value among the list of offers. Value of offers (in thousands of dollars): 409.9, 399.8, 412.5, 408.9, and 401.6.
median = 408.9
The mean income of a group of sample observations is $500; the standard deviation is $40. According to Chebyshev's theorem, at least what percent of the incomes will lie between $400 and $600? (Omit the "%" sign in your response.)
84%
Refer to the following frequency distribution on days absent during a calendar year by employees of a manufacturing company: Days Absent. Number of Employees 42 up to 47 60 47 up to 52 28 52 up to 57 11 57 up to 62 5 62 up to 67 1 How many employees were absent fewer than fifty two days?
88
For a symmetric and mound-shaped distribution with a mean of 130 and standard deviation of 20, approximately what percentage of the observations should we expect to lie between 90 and 170?
95.0 % of observations
An electronics firm sells two models of stereo receivers, two CD decks, and six speaker brands. When the three types of components are sold together, they form a "system." How many different systems can the electronics firm offer?
24
A coffee shop wants to know the relative popularity of different sizes for its drinks. A sample of drink orders has been organized into a frequency table. Use the table below to find the relative frequency for drink orders in a size medium. Enter your answer as a decimal rounded to three places. Size Frequency Small 5 Medium 29 Large 11
29/45 = .644
Molly's Candle Shop has several retail stores in the coastal areas of North and South Carolina. Many of Molly's customers ask her to ship their purchases. The following chart shows the number of packages shipped per day for the last 100 days. a.What is this chart called?
Histogram
Which one of the following is false about the range? A) it is easily calculated by simple subtraction B) it considers all of the data values C) it describes the distance between the highest and lowest data values D) it is a measure of dispersion
B) It only considers the largest and smallest data values.
A university president determines that both the average and the median time it takes students to finish a four-year degree at her institution is around 5.5 years. Which one of the following situations could this indicate? multiple choice The data seem to have a right skewed distribution. The data seem to have a left skewed distribution. The distribution of the data is possibly symmetric.
The distribution of the data is possibly symmetric.
Each salesperson in a large department store chain is rated on their sales ability and their potential for advancement. The data for the 500 sampled salespeople are summarized in the following table. Sales ability. Fair. Good Excellent Below 16 12 22 Average 45 60 45 Above 93 72 135 What is the probability that a salesperson selected at random has above average sales ability and has excellent potential for advancement?
The events are not independent. P(above average ability and excellent potential) = P(above average ability) P(excellent potential | above average ability) = (300/500) (135/300) = 135/500 = 0.27. 0.27
Each salesperson in a large department store chain is rated on their sales ability and their potential for advancement. The data for the 500 sampled salespeople are summarized in the following table. Sales ability. Fair. Good Excellent Below 16 12 22 Average 45 60 45 Above 93 72 135 What is the probability that a salesperson selected at random will have average sales ability and good potential for advancement?
The events are not independent. P(average ability and good potential) = P(average ability) P(good potential | average ability) = (150/500)(60/150) = 60/500 = 0.12. 0.12
The median for a left-skewed distribution is 68.5. Which of the statements below are correct? check all that apply The mean is less than 68.5. The mean is also 68.5. The mode is more than 68.5. The mean is more than 68.5.
The mean is less than 68.5. The mode is more than 68.5.
Starbucks is collecting information from its customers. Which of the following pieces of information are examples of quantitative data? You must make a selection for each option. Click once to place a check mark for correct answers and click twice to place an "x" for the wrong answers. check all that apply: The number of food items purchased by the customer The cost of the items purchased during the customer's visit The mode of payment (for example, credit card) The gender of the customer The amount of coffee ordered in ounces (for example, 8 oz, 12 oz, ...)
The number of food items purchased by the customer The cost of the items purchased during the customer's visit The amount of coffee ordered in ounces (for example, 8 oz, 12 oz, ...)
The classes for a frequency distribution are defined by two numbers called the _____________.
class limits
The ____________ for a class is the halfway point between the lower limit and the upper limit of the class.
class midpoint
A fashion designer organizes the results of a study on fall color trends into a pie chart. This action fits under the umbrella of inferential statistics.
false
Inferential statistics is a branch of statistics that involves using a complete set of data to make conclusions, estimations, or decisions about a different, complete set of data.
false
True or False: The number of injuries each month resulting from accidents at a company producing sheets of aluminum is carefully monitored. These monthly totals are an example of continuous data.
false
A designer sells a scarf in three different colors. In order to understand the sales of the colors of the scarf, the designer's team could create a _______________.
frequency table
The ________________ is a measurement or observation that repeats most often in the data set.
mode
The average age of a sample of custodial employees of a small holding company is 44. This is an example of a ________________.
statistic, because it summarizes sample data
Chebyshev's theorem does not assume symmetry in the distribution of the data and can be used on any data set.
true
If there are "m" ways of doing one thing, and "n" ways of doing another thing, the multiplication formula states that there are (m) × (n) ways of doing both.
true
Inferential statistics is the branch of statistics that involves using a subset of available data to make conclusions, estimations, or decisions about the larger data set.
true
True or False: A nutrition supplement company has created an herbal treatment for high blood pressure. It plans to conduct a series of double-blind clinical trials to determine if the supplement is effective at reducing blood pressure in hypertensive patients. In this situation, it is not possible for the company to test the supplement on every hypertensive person in the population.
true
True or False: An LED light bulb manufacturer wants to know the average lifetime of its bulbs. To estimate this average, it plans to run a test on the bulbs that involves running a higher than normal current through the bulbs until they burn out. In this situation, it is not reasonable to perform this measurement on the full population of bulbs to determine the true average lifetime.
true
True or False: Discrete data often result from counting the number of items belonging to a set.
true
True or False: Fuhu, the creator of an Android tablet for kids, would like to know the number of hours kids typically spend on the website YouTube. To estimate this quantity of interest, Fuhu monitors the browsing habits of a random selection of 500 of its users. The monitoring allows Fuhu to determine the amount of time each of these 500 users spent at YouTube. The data obtained from this monitoring is an example of sample data.
true
True or False: Relative class frequency is the fraction or proportion of observations that occur within a class.
true
True or False: The hospital administrator for a nearby hospital is reviewing hospital records to obtain the number of drug resistant bacteria infections in the hospital for every month over the past ten years. These monthly tallies are an example of discrete data.
true
True or False: The sentence below is an example of the use of descriptive statistics. A nurse creates a graph called a pie chart to display the types of infections patients develop and the relative frequency of those infections at the hospital where she works.
true
The standard deviation is defined as the square root of the ________.
variance
Variables W, X, Y, and Z all have the same mean, but W has a variance of 5.1 m². X has a variance of 2.3 m². Y has a variance of 9.4 m², and Z has a variance of 5.6 m². For which variable are the measurements most clustered around their mean? Y W X Z
x
There are 10 marbles in a jar. 5 marbles are red, 3 marbles are green, and 2 marbles are blue. Suppose two marbles are drawn consecutively from the jar without replacement. What is the probability that both marbles will be blue?
(2/10) * (1/9) = 0.0222
There are 10 marbles in a jar. 4 marbles are red, 3 marbles are green, and 3 marbles are blue. Suppose two marbles are drawn consecutively from the jar without replacement. What is the probability that both marbles will be red?
(4/10) * (3/9) = 0.1333
Refer to the following distribution of commissions: Monthly commissions. Class Frequencies $500-$700 5 700-900 8 900-1100 14 1100-1300 14 1300-1500 17 1500-1700 25 1700-1900 28 1900-2100 37 What is the relative frequency for those salespersons that earn from $1500 up to $1700?
.17
The probability a HP network server is down is .045. If you have three independent servers, what is the probability that at least one of them is operational? (Round your answer to 6 decimal places.)
.999909, found by 1 - (.045)3
Molly's Candle Shop has several retail stores in the coastal areas of North and South Carolina. Many of Molly's customers ask her to ship their purchases. The following chart shows the number of packages shipped per day for the last 100 days. 1. What is the total number of frequencies? 2. What is the class interval? 3. What is the class frequency of the 25 up to 30 class? 4. What is the relative frequency of the 25 up to 30 class? (Round your answer to 2 decimal places.) 5. What is the midpoint of the 20 up to 25 class? (Round your answer to 1 decimal place.) 6. On how many days were there 20 or more packages shipped?
1. 100 2. 5 3. 10 4. .10 5. 22.5 6. 31
If a sample of 1000 pieces is taken from a normal distribution (i.e., bell-shaped curve), how many pieces would be expected to lie between ± 1 standard deviations of the mean?
Per empirical rule, approx. 68% of pieces should lie between ±1 std. dev. of the mean. So 68% x 1000 pieces = 680 pieces
Explain the difference between qualitative and quantitive variables.
Qualitative data is not numerical, whereas quantitative data is numerical.
explain the difference between a sample and a population
A population is the entire group in interest. A sample is a subset taken from a population.
Transaction amounts at a particular stock brokerage firm have a mean of $1,250 and standard deviation of $140. Use Chebyshev's Theorem to answer the following questions. a. At least what percentage of the transactions should we expect to lie between $950 and $1,550? b. Compute the interval that would be expected to contain at least 15161516 of the transaction amounts. c. Compute the interval that would be expected to contain at least 3434 of the transaction amounts.
A) At least 78.22 % transactions B)Lower interval limit = $ 690. Upper interval limit = $ 1,810. C) Lower interval limit = $ 970. Upper interval limit = $ 1,530.
explain the difference between a discrete and a continuous variable
Discrete variables (e.g., number of customers, number of cars, etc.) can assume only certain values (often whole numbers such as 0, 1, 2, 3, ...). Continuous variables (e.g., weight, length, time, distance, diameter, etc.) can assume any value (including fractional) within a range. Discrete variables typically are counted, but continuous variables typically are measured or timed
Electricity companies offer rebates to consumers who invest in solar panel technology to power items in their home. To calculate the appropriate value of these rebates, the companies must determine the typical amount of sunlight each region receives over the course of the year. For example, one town in Arizona receives an average of 3,806 hours of sunlight each year. This town's number of sunlight hours follows a bell-shaped distribution with a standard deviation of 342 hours. Provide an interval that will contain the number of sunlight hours for approximately 68% of the years in this town.
Lower interval value = 3464 hours. Upper interval value = 4148 hours.
A landscaping business has several new maintenance contracts. Find the median value among the list of new maintenance contracts. Value of contracts (in thousands of dollars): 20.1, 5.3, 12.0, 13.8, 10.2, 4.0, and 3.8.
Median = 10.2
If P(A) = 0.62, P(B) = 0.47, and P(A or B) = 0.88, then P(A and B) = _____.
P(A or B) = P(A) + P(B) - P(A and B). P(A and B) = P(A) + P(B) - P(A or B) = 0.62 + 0.47 - 0.88 = 0.21. P(A and B) = 0.21. 0.2100
Each of three independent file servers has a reliability (i.e., probability of operating correctly) of 92%. At least one server must be operational to run the web site. The overall web site reliability is ______:
P(Website Works) = 1 - P(Website Doesn't Work) = 1-P(All 3 servers fail) = 1 - (1-0.92)3 = 0.999488 (or 99.9488%).
Consider the following 8 data values: 6, 7, 10, 12, 14, 16, 21, 58. The range and the median are:
Range = 58 - 6 = 52. Median = (12+14) / 2 = 13
If two dice are rolled simultaneously, the probability of rolling a total of 9 is approximately ________:
Recall sample space of 36 possible outcomes for rolling a dice twice. 4 of them will give total of 9. So probability is 4 / 36 = 0.1111.
For which data sets below would the median be a better choice than the mean as a measure of the center? Circumference of Male Waists (in inches): {30.0, 35.5, 36.0, 32.5, 32.0, 37.5, 41.5, 38.5} Salaries (in thousands): {$40.2, 55.8, 405.1, 55.9, 28.4, 37.7, 50.9} Quantity of French Fries Eaten (in grams): {165, 159, 164, 160, 162, 161, 158, 165, 168, 167}C Home values (in thousands): {$155.6, 2,107.2, 210.0, 215.3, 187.1, 270.3, 250.6}
Salaries (in thousands): {$40.2, 55.8, 405.1, 55.9, 28.4, 37.7, 50.9} Home values (in thousands): {$155.6, 2,107.2, 210.0, 215.3, 187.1, 270.3, 250.6}
Measurements from a sample are called ______:
Sample measurements are called statistics.
Calculate the sample standard deviation for the following set of data from a local restaurant. The values represent the number of reservations for the slowest day of the week: 5, 7, 3, 9, 11, 10, 2, and 5.
Sample standard deviation = 3.295 reservations
The following data set is from test results for a car's fuel economy (measured in miles per gallon): 40.3, 43.4, 44.5, 35.8, 39, and 44.3. Calculate the sample standard deviation for the fuel economy data.
Sample standard deviation = 3.468 miles per gallon
The following values are from a Business Statistics exam. Nine students took the exam. Calculate the sample standard deviation for the set of scores: 65, 50, 90, 95, 90, 85, 80, 70, and 75.
Sample standard deviation for the set of scores = 14.386
Which of the following statements describe weaknesses of the Range as a measure of dispersion? It is easy to interpret. Several data sets that have very different levels of dispersion could easily have the same range. It is insensitive to differences in dispersion for data sets that have similar differences between their smallest and largest values. It is easy to calculate.
Several data sets that have very different levels of dispersion could easily have the same range. It is insensitive to differences in dispersion for data sets that have similar differences between their smallest and largest values.
A large jar contains 44 marbles. 16 of these marbles are red, 16 marbles are green and 12 marbles are blue. a. If two marbles are randomly drawn in succession (the first marble is not returned to the jar), what is the probability that both marbles will be red? b. If two marbles are randomly drawn in succession (the first marble is not returned to the jar), what is the probability that both marbles will be green? c. If two marbles are randomly drawn in succession (the first marble is not returned to the jar), what is the probability that neither marble will be blue? d. If two marbles are randomly drawn in succession (the first marble is not returned to the jar), what is the probability that the first marble will be blue and the second marble will be green? e. Suppose three marbles are randomly drawn in succession (the first two marbles are not returned to the jar). What is the probability that all three marbles will be red?
Since previously drawn marbles are not returned to the jar before drawing the next marble, this problem uses the multiplication rule for dependent events. In other words, the probability of getting a specific marble color on the next draw depends on which marble color was selected on the previous draw. The multiplication rule for dependent events has the following form: P(A and B)=P(A)P(B|A)P(A and B)=P(A)P(B | A) . a. P(First two are red)=P(First is red)P(Second is red ∣∣First is red) = 16/44 · 15/43 =0.127. b. P(First two are green)=P(First is green)P(Second is green ∣∣First is green)=16/44 · 15/43=0.127. c. P(Neither are blue)=P(First is not blue)P(Second is not blue ∣∣first is not blue)=32/44 · 31/43=0.524. d. P(First is blue and Second is green)=P(First is blue)P(Second is green ∣∣ First is blue)=12/44 · 16/43=0.101. e. Three or more events involves a simple extension to the multiplication rule for two dependent events: P(A and B and C)=P(A)P(B|A)P(C |A and B) Fortunately, this rule is easier to use than to write! P(First three are red)= 16/44· 15/43· 14/42=0.042.
Below are 10 data values representing commute distance to work (in miles) for a sample of 10 employees. 8.1, 2.7, 4.6, 10.6, 18.4, 24.0, 8.0, 22.1, 19.4, 3.4 a. Calculate the range for the above set of distances. b. Calculate the sample variance for the above set of distances. c. Calculate the sample standard deviation for the above set of distances.
a) range = 21.3 b) sample variance = 65.549 c) sample standard deviation = 8.096
a. The motor vehicle department in a particular state has license plates which contain six characters. Each of the first two characters can be any letter (A-Z). Each of the next two characters can be any letter (A-Z) or digit (0-9). Each of the last two characters can be any letter (A-Z). How many different license plates can be printed? b. An automotive dealership offers a particular model of vehicle in 6 different exterior colors, 2 different interior colors and with 5 different option packages. In how many configurations can this vehicle be ordered? c. Jeffrey has jackets in 2 different colors, shirts in 4 different colors, trousers in 4 different colors and ties in 5 different colors/patterns. How many different outfits can Jeffrey make (assuming he doesn't care how well the clothing items will coordinate with each other)?
These questions all pertain to the Fundamental Counting Rule, since we are interested in how many possible outcomes exist for a series of steps (events) in which each event can happen in a particular number of ways (options). a. 26 x 26 x 36 x 36 x 26 x 26 = 592,240,896 license plates. b. 6 x 2 x 5 = 60 configurations. c. 2 x 4 x 4 x 5 = 160 outfits.
a. Suppose that 44% of American CEO's are women. Furthermore, suppose that 22% of American CEO's are women under the age of 40. Given that a randomly selected American CEO is a woman, what is the probability that she is under the age of 40? b. The probability that the head of a U.S. household has a life insurance policy is 0.470. Moreover, the probability that the head of a U.S. household has a life insurance policy and is over the age of 50 is 0.390. Given that a randomly selected head of a U.S. household has a life insurance policy, what is the probability that he/she is over the age of 50? c. Suppose that 22% of customers purchase peanut butter during a particular trip to the grocery store. Furthermore, 19% of grocery store customers purchase both peanut butter and jelly. Given that a random grocery store customer purchases peanut butter, what is the probability that he/she also purchases jelly during this trip? d. In a particular convenience store, the probability that a customer will purchase beer is 0.300. Moreover, given that the customer has purchased beer, the probability that he/she will purchase pretzels is 0.230. What is the probability that a random customer in this convenience store will purchase beer and pretzels together?
These questions involve the conditional probability rule P(A ∣∣ B)=P(A and B)P(B)P(A | B)=P(A and B)P(B) . a. P(Under 40 ∣∣Woman)=P(Under 40 and Woman)P(Woman)=22/44=0.500. b. P(Over 50 ∣∣Life insurance)=P(Over 50 and Life insurance)P(Life insurance)=0.390/0.470=0.830. c. P(Jelly ∣∣Peanut butter)=P(Jelly and Peanut butter)P(Peanut butter)=19/22=0.864. d. P(Pretzels ∣∣Beer)=P(Pretzels and Beer)P(Beer).P(Pretzels | Beer)=P(Pretzels and Beer)P(Beer). Therefore, solving algebraically, P(Pretzels and Beer)=P(Beer)P(Pretzels |Beer)=(0.300)(0.230)=0.069.
If two events represent all possible outcomes that can happen, those events are called __________:
They are collectively exhaustive events
If one event has no effect on the probability of another event, those events are called ___________:
They are independent events.
If two events cannot both happen at the same time, those events are called ____________:
They are mutually exclusive events
The number of complaints registered each month at the local Post Office during the last 26 months are: 46 36 37 34 33 17 36 31 44 94 77 53 30 36 21 44 26 36 19 21 38 18 32 26 11 a. (4 points) Construct a frequency distribution (use frequencies, not relative frequencies). Start the first class interval at 0 and use an interval width of 10! Note: you don't need to compute how many classes to use here, since your last class interval will include the highest data value. b.(5 points) Properly construct a histogram using the above frequency distribution. Again, plot frequencies (not relative frequencies). Label the chart properly with values.
a) Class. Frequency 0 ≤ x < 10 2 10 ≤ x < 20 4 20 ≤ x < 30 4 30 ≤ x < 40 11 40 ≤ x < 50 4 50 ≤ x < 60 1 b) frequency on the tall left x axis class on the y horizontal axis
Jennifer has recently interviewed for two different jobs. She feels there is a 0.320 probability of being offered the first job and a 0.620 probability of being offered the second job. Assume that the two job offers are statistically independent. a. What is the probability that Jennifer will be offered both jobs? b. What is the probability that Jennifer will be offered neither of those two jobs? c. What is the probability that Jennifer will be offered at least one of the two jobs? d. What is the probability that Jennifer will be offered the first job but not the second job? e. What is the probability the Jennifer will not be offered the first job but will be offered the second job?
This problem uses the multiplication rule for independent events: P(A and B)=P(A)P(B).P(A and B)=P(A)P(B). a. P(First job offered and Second job offered)=P(First job offered)P(Second job offered)=(0.320)(0.620)=0.198. b. Since the probability of being offered the first job = 0.320, the probability of not being offered it is 1 − 0.320 = 0.680. Since the probability of being offered the second job = 0.620, the probability of not being offered it is 1 − 0.620 = 0.380. Therefore, we apply the multiplication rule using these probabilities: P(First job not offered and Second job not offered)=P(First job not offered)P(Second job not offered)=(0.680)(0.380)=0.258. c. Being offered at least one of the two jobs is the complement of being offered neither of the two jobs. Therefore: P(At least one job offered)=1−P(Neither job offered)=1−0.258=0.742. d. P(First job offered and Second job not offered)=P(First job offered)P(Second job not offered)=(0.320)(0.380)=0.122. e. P(First job not offered and Second job offered)=P(First job not offered)P(Second job offered)=(0.680)(0.620)=0.422.
A sales representative calls on four hospitals in Westchester County. It is immaterial what order he calls on them. How many ways can he organize his calls?
Use the multiplication formula: (4)(3)(2)(1) = 24. 24
Your favorite soccer team has two remaining matches to complete the season. The possible outcomes of a soccer match are win, lose, or tie. What is the possible number of outcomes for the season?
Use the tree diagram to determine the possible outcomes, which are: {W,W},{W,L},{W,T},{L,W},{L,L},{L,T},{T,W},{T,L},{T,T}. There are 9 possible outcomes. 9
A recent survey reported in BusinessWeek dealt with the salaries of CEOs at large corporations and whether company shareholders made money or lost money. CEO PaidMore Than$1 MillionCEO PaidLess Than$1 MillionTotal Shareholders made money3 15 18 Shareholders lost money5 5 10 Total8 20 28 If a company is randomly selected from the list of 28 studied, calculate the probabilities for the following : (a)The CEO made more than $1 million. (Round your answers to 3 decimal places.) (b) The CEO made more than $1 million or the shareholders lost money. (Round your answers to 3 decimal places.) (c) The CEO made more than $1 million given the shareholders lost money. (Round your answers to 3 decimal places.) d) Select 2 CEOs and find that they both made more than $1 million. (Round your answers to 3 decimal places.)
a) .286, found by 8/28 b) .464, found by (8 + 10 - 5)/28 c) .500, found by 5/10 d) .074, found by (8/28)*(7/27)
Consider these five values of a population: 6, 3, 6, 3, and 6. (a)Determine the mean of the population. (Round your answer to 1 decimal place.) (b)Determine the variance of the population. (Round your answer to 2 decimal places.)
a) 4.8 b) 2.16
The events AA and BB are mutually exclusive. Suppose P(A)=.27P(A)=.27 and P(B)=.35.P(B)=.35. (a)What is the probability of either AA or BB occuring? (Round your answer to 2 decimal places.) b)What is the probability that neither AA nor BB will happen? (Round your answer to 2 decimal places.)
a) P(A or B) = P(A) + P(B)=.27+.35=.62 .62 b) P(neither)=1−.62=.38 .38
a. A professional football kicker has a 96.2% probability of successfully kicking an extra point after a touchdown. Assuming statistical independence, what is the probability that this kicker will successfully make all of his next nine extra point kicks? b. What is the probability that the kicker will miss at least one of his next nine extra point kicks? c. A professional golfer has a 89.50% probability of making a 5-foot putt. Assuming statistical independence, what is the probability that this golfer will successfully make all of his next ten 5-foot putts?
a) P(Making all kicks)=(0.962)9=0.7056. b) P(Missing at least one kick)=1−P(Making all kicks)=1−0.7056=0.2944. c) P(Making all putts)=(0.8950)^10=0.3298. d)P(Missing at least one putt)=1−P(Making all putts)=1−0.3298=0.6702
Below are the ages (in years) of seven random attendees at a carnival. 18, 17, 16, 12, 13, 11, 16 a. Calculate the mean for the above set of ages. b. Calculate the median for the above set of ages. b. Calculate the mode for the above set of ages.
a) mean = 14.71 b) median = 16 c) mode = 16
A sample of 25 undergraduates reported the following dollar amounts of entertainment expenses last year: 698 745 752 773 710 720 719 705 754 719 702 711 705 742 738 685 709 713 743 696 774 740 762 758 729 (a)Find the mean, median and mode of this information. (Round your answers to 2 decimal places. Omit the "$" sign in your response.) (b)What are the range and standard deviation? (Do not round your intermediate calculations. Round your final answers to 2 decimal places. Omit the "$" sign in your response.) (c)Use the Empirical Rule to establish an interval which includes about 95 percent of the observations. (Round your answers to 2 decimal places. Omit the "$" sign in your response.)
a) mean = 728.08 median = 720 mode = 705 and 719 b) range = 89 Standard deviation = 25.28 c) the interval is from 677.25 up to 778.64
A country club has 252 members. The frequency distribution of their ages is shown below: Age (years). Number of members Under 30 21 30-39 37 40-49 60 50-59 55 60-69 57 70-over 22 Total 252 a. What is the probability that a randomly selected member is 30 to 39 years old? b. What is the probability that a randomly selected member is 50 years of age or older? c. What is the probability that a randomly selected member is 39 years of age or younger? d. What is the probability that a randomly selected member is not between 60 to 69 years old?
a. P(30 to 39)= 37 / 252=0.147 b. P(50 or over)= (55 + 57 + 22)/252 = 134/252 =0.532 c. P(39 or younger)= (21+37)/252 = 58/252 = 0.230. d. P(Not 60 to 69)=1−P(60 to 69) = 1−57/252 =0.774.
Below is a contingency table showing membership at a local gym based on gender and age group. Under 30 30-49 50 or more Total Male 48 32 30 110 Female 47 35 27 109 Total 95 67 57 219 a. What is the probability that a randomly selected gym member is male or under 30 years of age? b. What is the probability that a randomly selected gym member is female or 30-49 years of age? c. Given that a randomly selected gym member is male, what is the probability of being under 30 years of age? d. Given that a randomly selected gym member is under 30 years of age, what is the probability of being female? Round your answer to three decimal places. Probability = 0.431 Numeric Response 4.Edit Unavailable. 0.431 incorrect. e. What is the probability that a randomly selected gym member is female and 50 or more years of age?
a. P(male or under 30)= 110/219 + 95/219 − 48/219=0.717 b. P(female or 30-49)= 109/219 + 67/219 − 35/219 =0.644 c. P(under 30 ∣∣ male)= 48/110 =0.436 d. P(female | under 30)= 47/95 =0.495 e. P(female and 50 or more)= 27/219 =0.123
Below is a contingency table showing housing status (rent or own) for a sample of 382 community residents based on annual income (k = thousands of dollars). Under $50k. $50k−$80k. Over $80k Total Rent. 89 66 32 187 Own 42 88 65 195 Total. 131 154. 97. 382 a. What is the probability that a random community resident owns housing or earns $50k to $80k per year? b. What is the probability that a random community resident rents housing or earns under $50k per year? c. Given that a random community resident owns housing, what is the probability that he/she earns $50k to $80k per year? d. Given that a random community resident earns $50k to $80k per year, what is the probability that he/she rents housing? e. What is the probability that a random community resident rents housing and earns under $50k per year?
a. P(owns or $50k to $80k)= 195/382 + 154/382 − 88/382 =0.683. b. P(rents or under $50k)= 187/382 + 131/382 − 89/382 =0.599. c. P($50k to $80k ∣∣ owns)=88/195=0.451. d. P(rents | $50k to $80k)=66/154=0.429. e. P(rents and under $50k)=89/382=0.233.
a. Suppose that a six-sided die (numbered 1-6) is rolled one time. What is the probability of rolling a 6? b. Suppose that a six-sided die (numbered 1-6) is rolled one time. What is the probability of rolling a 4 or lower? c. Suppose that a six-sided die (numbered 1-6) is rolled two times. What is the probability that the sum of the two rolls will be a 7? d. Suppose that a six-sided die (numbered 1-6) is rolled two times. What is the probability that the average of the two rolls will be a 4 or higher?
a. Since rolling a 6 represents 1 outcome out of a total of 6 possible outcomes, the probability is 16=0.167.16=0.167. b. Rolling a 4 or lower represents 4 outcomes (1 or 2 or 3 or 4) out of a total of 6 possible outcomes. Therefore, the probability is 46=0.667.46=0.667. c. There are 6 x 6 = 36 possible outcomes when rolling a die two times as follows: (1st roll, 2nd roll)(1, 1)(2, 1)(3, 1)(4, 1)(5, 1)(6, 1)(1, 2)(2, 2)(3, 2)(4, 2)(5, 2)(6, 2)(1, 3)(2, 3)(3, 3)(4, 3)(5, 3)(6, 3)(1, 4)(2, 4)(3, 4)(4, 4)(5, 4)(6, 4)(1, 5)(2, 5)(3, 5)(4, 5)(5, 5)(6, 5)(1, 6)(2, 6)(3, 6)(4, 6)(5, 6)(6, 6) Converting the above table of outcomes into a table of sums (totals) results in the following: Sums234567345678456789567891067891011789101112 From this table, we can see that rolling a sum of 7 represents 6 outcomes out of a total of 36 possible outcomes. Therefore, the probability is 636=0.167.636=0.167. d. Converting the table of outcomes in Part c into a table of averages results in the following: Averages1.01.52.02.53.03.51.52.02.53.03.54.02.02.53.03.54.04.52.53.03.54.04.55.03.03.54.04.55.05.53.54.04.55.05.56.0 From this table, we can see that rolling an average of 4 or higher represents 15 outcomes out of a total of 36 possible outcomes. Therefore, the probability is 1536=0.417.
a. The president of a large company wants to form an Executive Steering Committee to advise the company concerning important matters. This committee will consist of three managers selected from an overall pool of 17 managers. Assuming the order in which the three managers are selected to join the committee does not matter, how many different Executive Steering Committees are possible? b. In Part a, suppose each of the three managers selected to serve on the Executive Steering Committee will have a particular title (Chairman, Vice Chairman, Outreach Coordinator, etc.). In other words, the order in which the managers are selected for the various committee positions (titles) matters. In this case, how many possible Executive Steering Committees are possible? c. In a lottery game, three balls are randomly drawn from a machine containing 23 balls numbered from 1 to 23. To play the game, a player must purchase a lottery ticket in advance with three numbers on it of his/her choosing (numbered from 1 to 23). Subsequently, if the three numbers on the lottery ticket match the three numbers that are drawn from the machine (in any order), then the player will win the lottery. Assuming the order in which the numbers are drawn from the machine does not matter, how many possible outcomes (sets of three numbers) exist each time the game is played? d. Based on your Part c result and assuming the player only purchased one lottery ticket, what is the probability that he/she will win the lottery?
a. This problem pertains to combinations since we are interested in how many subsets of r = 3 items exist when selected from a set of n = 17 items when order does not matter. Therefore: rCn = n! / r!(n−r)! = 17! /(3)!(17−3)! = 680committees b. This problem pertains to permutations since we are interested in how many subsets of r = 3 items exist when selected from a set of n = 17 items when order matters. Therefore: rPn= n!/(n−r)!= 17! / (17−3)! =4,080 committees c. This problem pertains to combinations since we are interested in how many subsets of r = 3 balls exist when drawn from a machine containing n = 23 balls when order does not matter. Therefore: rCn=n! / r!(n−r)!=23! / 3!(23−3)! = 1,771 outcomes d. Using the Classical Approach to probability, if one ticket is purchased, the probability of winning is 1/1,771=0.000565.
a. A sample of 200 New York City sports fans has found that 115 fans have attended a Yankees game(s) during the current season, 65 fans have attended a Mets game(s), and 20 fans have attended both a Yankees and Mets game(s). Compute the probability that a randomly selected New York City sports fan has attended either a Yankees game or a Mets game during the current season. b. Based on current course performance, Mary feels that she has a 0.700 probability of passing Statistics, a 0.750 probability of passing Marketing, and a 0.580 probability of passing both Statistics and Marketing. What is the probability that Mary will pass at least one of these two courses? c. The Human Resources Department at a small company has reviewed the annual merit evaluations of 210 employees. 48 of these employees were told that their performance needs improvement, 35 employees were told that their attendance needs improvement, and 21 employees were told that both their performance and attendance needs improvement. What is the probability that a randomly selected employee was told that his/her performance or attendance needs improvement?
a. This question pertains to the Addition Rule of probability because we are looking for the probability of attending a Yankees game or a Mets game. Therefore: P(YankeesorMets)=P(Yankees)+P(Mets)−P(YankeesandMets)= 115/200 + 65/200 − 20/200=0.800. b. This question also pertains to the Addition Rule of probability because we are looking for the probability of passing statistics or passing marketing (i.e., passing at least one of those two courses). Therefore: P(PassStatisticsorPassMarketing)=P(PassStatistics)+P(PassMarketing)−P(PassStatisticsandMarketing)=0.700+0.750−0.580=0.870 c. This question also pertains to the Addition Rule of probability because we are looking for the probability of performance needing improvement or attendance needing improvement. Therefore: P(PerformanceorAttendanceneedsimprovement)=P(Performanceneedsimprovement)+P(Attendanceneedsimprovement)−P(PerformanceandAttendanceneedsimprovement)= 48/210 + 35/210 − 21/210 =0.295.
a. George, a college freshman, is debating what to do immediately after graduation. He feels there is a 0.411 probability that he will go to medical school. On the other hand, he feels there is a 0.357 probability that he will go to law school. Using George's probability estimates, what is the probability that he will go to medical school or law school immediately after graduation? b. In Part a, what is the probability that George will not choose either of those two options (medical school or law school) immediately after graduation? c. A batch of 180 parts in a production process is known to contain 6 parts that are underweight, 6 parts that are overweight, and 168 parts that are within the required weight specifications. If a single part is randomly selected from this batch, what is the probability that this part will be underweight or overweight? d. In Part c, what is the probability that the part selected will be within the normal weight specifications?
a. This question uses the Addition Rule of probability because we are looking for the probability of going to medical school or going to law school. Note that the intersection (overlap) probability P(medical school and law school) is zero since these two events are mutually exclusive. Therefore: P(Medical school or Law School)=P(Medical school)+P(Law school)=0.411+0.357=0.768. b. This question is asking for the complement of the question posed in Part a. Therefore: P(Neither Medical school nor Law school)=1−P(Medical school or Law school)=1−0.768=0.232. c. This question uses the Addition Rule of probability because we are looking for the probability of selecting an underweight part or overweight part. Note that the intersection (overlap) probability P(underweight and overweight) is zero since these two events are mutually exclusive. Therefore: P(Underweight or Overweight)=P(Underweight)+P(Overweight)=6/180+6/180=0.067. d. Since underweight, overweight and within represent all possible outcomes (i.e., are collectively exhaustive), this question is asking for the complement of the question posed in Part c. Therefore: P(Within weight specification)=1−P(Underweight or overweight)=1−0.067=0.933. Note: this answer can also be computed by P(Within weight specification)=168/180=0.933.
A travel agency has surveyed 50 customers regarding what their preferred vacation destination would be: the beach, the mountains, a big city or taking a cruise. The results are shown below. Customer Preferred Destination 1 Beach 2 Cruise 3 Beach 4 Mountains 5 Beach 6 BigCity 7 Cruise 8 Mountains 9 Beach 10 Beach 11 Beach 12 Mountains 13 Cruise 14 Mountains 15 BigCity 16 Mountains 17 Cruise 18 Cruise 19 Beach 20 Mountains 21 Beach 22 Beach 23 Cruise 24 Beach 25 Mountains 26 Beach 27 Beach 28 Mountains 29 Beach 30 Beach 31 Beach 32 Big City 33 Cruise 34 Mountains 35 BigCity 36 Beach 37 Mountains 38 Cruise 39 Cruise 40 Mountains 41 BigCity 42 Beach 43 Mountains 44 Beach 45 Mountains 46 Cruise 47 Mountains 48 Big City 49 Big City 50 Mountains a. Complete the frequency table below using this data b. Based on these results, which vacation destination was most popular among the customers surveyed? c. Based on these results, which vacation destination was least popular among the customers surveyed?
a. beach 18 .36 mountains 15 .30 bigcity 7 .14 cruise 10 .20 total 50 100 b. beach c. big city
250 random U.S. drivers (male and female) were asked whether they own an American brand or foreign brand vehicle. The results are as follows: American Foreign Total Male 70 50 120 Female 70 60 130 Total 140 110 250 One driver is randomly sampled from the 250 drivers asked. Compute the following probabilities (you can leave them as fractions if you prefer). a.(2 points) Probability the driver owns an American brand vehicle. b.(2 points) Probability the driver is female AND owns an American brand vehicle. c.(2 points) Probability the driver is male OR owns a foreign brand vehicle. d.(2 points) Given the driver owns a foreign brand vehicle, the probability of being female. e.(2 points) Given the student is male, the probability he owns an American brand vehicle.
a)140/250 b)70/250 c)(120/250) + (110/250) ‒ (50/250) = 180/250 d)60/110 e)70/120