Statistics Do Now's
Explain extrapolation.
Extrapolation is prediction beyond the range of observations.
Ten students took an aptitude test in technical electronics. There were 1,000 possible points. The scores were are follows: 351 988 348 450 290 965 360 346 332 318 ( a) Compute the mean of all ten scores. ( b) Compute the median of all ten scores and compare your answers to that of part ( a). ( c) If all ten scores were to be used, which average (mean or median) would best describe most of the students? ( d) Compute a 10% trimmed mean. ( e) Which of the three averages best describes most of the students?
( a) Mean = 474.8 points ( b) Median = 349.5 points; The median is less than the mean. ( c) The median ( d) Trimmed mean = 433.75 points ( e) The median; 349.5 points
|x = 200 ( mean) x= 50 Find: μ - 30 to μ + 30
50 -350
From the information found in the Statistical Abstract of the United States (117th edition) it was determined that the median income for households in each of the fifty states, in thousands of dollars, has mean μ= 33.81 and standard deviation σ = 5.10. ( a) Use Chebyshev's Theorem to find an interval in which at least 75% of the states' median incomes will lie. ( b) Use Chebyshev's Theorem to find an interval in which at least 93.8% of the states' median income lie.
( a) 23.61 thousand to 44.01 thousand ( b) 13.41 thousand to 54.21 thousand
Home Security Systems is studying the time utilization of its sales force. A random sample of 40 sales calls showed that the representatives spend an average (mean) time of 42 minutes on the road for each sales call. The standard deviation of the call times is 5 minutes. ( a) Compute the coefficient of variation (CV) for this data. ( b) Use Chebyshev's Theorem to find the smallest time interval in which we can expect to find at least 75% of the data.
( a) CV = 11.9% ( b) Interval from 32 minutes to 52 minutes
Myra did a study of the number of weeks 10 novels were on a national best-seller list. The results were as follows: 7 15 48 2 12 20 10 15 102 24 ( a) compute the mean, the median, and the mode of this data set. ( b) Compute a 10% trimmed mean for the data set. ( c) How did the extreme values affect each average?
( a) Mean = 25.5; median = 15; mode = 15 ( b) Trimmed mean = 18.9 ( c) The extreme values increased the mean noticeably. They did not affect the median or the mode.
According to data provided by the Statistical Abstract of the United States (117th edition), the number of daily newspapers in the five states in the midwest has a mean μ= 30.8 and standard deviation σ = 38.3. For five states in the Pacific region μ2 = 61.4 with standard deviation σ2 = 19.07/ ( a) Compute the coefficient of variation for each region. ( b) Which region has the greater variation in the number of newspapers as a fraction of the mean?
( a) Midwest: CV = 124.4%; Pacific Region: CV = 31.06% ( b) The midwest region has greater variability.
How many sequences of three letters can you make from the letters {A, B, C, D, E} if ( a) The letters must all be different. ( b) Repetitions are allowed.
( a) Number of sequences = P(5,3) = 60 ( b) Number of sequences = 5^3 = 125
( a) How many ways can you choose a panel of 5 judges from a pool of 10 different judges? ( b) How many ways can you seat the five judges in a row?
( a) Number of ways = C(10,5) = 252 ( b) Number of ways = P(5,5) = 5! = 120
( a) How would you use a random number table to get a random sample of 8 families from a subdivision? The subdivision contains 92 families. ( b) Use the line from random number table below to identify the first five families in your sample. 66330 33393 95261 95349
( a) Number the families from 01 to 92. Read consecutive groups of two digits until you have twelve distinct numbers from 1 to 92. ( b) 66, 33, 03, 93, 85
( a) Describe how you would use a random number table to get a random sample of 12 men's dress shirts taken from a shipment of 475 men's dress shirts. ( b) Use the line from the random number table given below to identify the first seven shirts in your sample. 08811 82711 57392 25252 30333
( a) Number the shirts from 001 to 475. Read consecutive groups of three digits until you have twelve distinct numbers from 1 to 475. ( b) 088, 118, 271, 157, 392, 252
An insurance company wants to know the proportion of medical doctors in New York involved in at least one malpractice suit in the last three years. They survey a random sample of 200 medical doctors in New York. ( a) What is the population? ( b) What is the sample? ( c) Could the insurance company generalize and say that this sample is representative of all medical doctors in rural areas of the country? Why or why not?
( a) Population: The response (has or has not been involved in a malpractice suit in the last three years) from all medical doctors in New York. ( b) Sample: The responses to the same question from the 200 medical doctors in the survey. ( c) No. The sample was not restricted to medical doctors from rural areas in New York. Many of those in the sample could have come from New York City.
English 105: Great Writers of America has 447 students. To estimate the amount of time students in this section spent studying for the midterm exam a random sample of 40 students were surveyed. ( a) What is the population? ( b) What is the sample? ( c) Would this sample necessarily be representative of the time students enrolled in English 105 spent studying for the comprehensive final exam? Why or why not?
( a) Population: The times spent studying for the midterm exam by the 447 students in English 105. ( b) Sample: The times spent studying for the midterm exam by the 40 students surveyed. ( c) No. Students would probably spend more time studying for a comprehensive final exam than they would for a midterm.
Goldilocks goes into a cottage and find a bowl of porridge. The odds of the porridge being too hot is .40, the and odds of it being too cold is .30. If it isn't too hot or too cold, it's just right. ( a) Are these mutually exclusive events? Why? ( b) What is the probability of the bowl being just right temp.?
( a) They are mutually exclusive, because they are dependent. The porridge can only be either too hot, too cold, or just right. They can not be all the same at once. ( b) .30 chance of the bowl of porridge being just right.
Find the area between z = 1.63 and z = 1.94. (Please round your answer to four decimal places.)
0.0253
Find the slope of the least square line if: The pearson product-moment correlation is .7902 The standard deviation of the response variable is .2722 And the standard deviation of the explanatory variables is 7.347
0.02928
A biologist is studying a new hybrid tomato. It is known that the seeds of this hybrid tomato have probability of 0.48 germinating. The biologist plants 10 seeds. What is the probability that at least 8 seeds will germinate? (Please round your answer to three decimal places.)
0.042
Dr. Strasen developed a test to measure boredom tolerance. He administered it to a group of 4,982 adults between the ages of 21 and 40. The possible scores were 0, 1, 2, 3, and 4, with 4 indicating the highest tolerance for boredom. The test results for the group are shown below. Score Number of Subjects 0 708 1 1732 2 1795 3 688 4 59 What is the probability that someone in the group who took the test made either a 3 or 4? (Please round all intermediate steps to two decimal places.)
0.15
Privacy is a concern for many users of the Internet. One survey showed that 52% of Internet users are somewhat concerned about the confidentiality of their e-mail. Based on this information, what is the probability that for a random sample of 11 Internet users, 6 are concerned about the privacy of their e-mail? (Please round your answer to three decimal places.)
0.233
Sociologists say that 45% of married women claim that their husband's mother is the biggest bone of contention in their marriages. Suppose that five married women are having coffee together one morning. Using a table, what is the probability that at least three of them dislike their mother-in-law? (Please round your answer to three decimal places.)
0.407
The percentage of American men who say they would marry the same woman if they had to do it all over again is 74%. The percentage of American women who say they would marry the same man if they had to do it all over again is 82%. What is the probability that in a group of 9 married men, at least 7 will claim that they would marry the same woman again? (Please round your answer to three decimal places.)
0.573
Tickets numbered 1 to 20 are shuffled and a ticket is drawn at random. What is the probability that they ticket drawn has a number which is a multiple of 2 and is also a multiple of 5? What is the probability that the ticket drawn has a number which is a multiple of 2 OR of 5?
0.6
After examining daily receipts over the past year, it was found that the Green Parrot Italian Restaurant has been grossing over $2644 a day for about 30% of its business days. Using this as a reasonably accurate measure, find the probability that the Green Parrot will gross over $2644 fewer than 3 days in the next 5 business days. (Please round your answer to three decimal places.)
0.837
For the following, state whether the variable is continuous or discrete. 1. The number of cars sold by a dealership. 2. The length of a leaf. 3. Number of senators in the United States Senate. 4. The time, rounded to the nearest hour, that this class ends at. 5. The surface area of a desk.
1. Discrete. 2. Continuous. 3. Discrete. 4. Discrete. 5. Continuous.
Barry, Lupe, Julio, Jim, and Maria are in the math club. The club advisor will assign students to 3-person teams at the next Math Team competition. How many 3-person teams can be formed from these five students?
10
NO CALC. Find the outliers in the data. Then find the mean when outliers are included and again when they are not included. If there are no outliers, find the mean of the data. 76, 69, 79, 23, 74, 66, 77, 73, 115, 73
115 and 23 are outliers; mean with outliers = 72.5; mean without outliers = 73.375
Survey about art programs. 250 want after school. 150 want day. 100 want none. Measure of angle in after school group?
180 degrees.
What are the stems for the data set 54, 43, 58, 25, 67, 36, 61?
2, 3, 4, 5, 6
Nine aspiring athletes will be selected out of 17 trying out for their school basketball team. How many different groups of nine are there?
24,310
From a committee of 6 women and 5 men, two names are drawn to lead the committee. What is the probability that both people drawn will be women?
3/11
Find the upper quartile, lower quartile, and interquartile range for the set of data. 23, 37, 31, 18, 26, 14, 33, 13
32, 16, 16
For the past 15 days, the housekeeping unit has reported the number of rooms not ready by 3:30 PM. The director of housekeeping is aware that the distribution is symmetrical and bell-shaped. It is approximately normal, with mean μ = 25.5 and standard deviation σ = 2.5. If housekeeping needed to make a control chart for the reported data what would be the highest control limit?
33
If you choose an answer to this question at random, what is the chance you will be correct? A. 25% B. 50% C. 60% D. 25%
33%
The number of hours required in each discipline... History = 8 hours Math = 10 hours English = 12 hours Health = 9 hours Political Science = 5 hours What is the percentage of time required for English discipline?
45.3 %
Suppose you are choosing a 4-digit personal access code. This code is made up of 2 numbers (1-9 which can be repeated), followed by 2 letters (A-Z which also can be repeated). Find the total number of possibilities.
54,756
Find the population standard deviation σ: 14, 16, 18, 22, 5, 12, 4, 20, 6
6.32
A committee is to the committee, how many different committees can be formed consist of two members. If there are seven men and six women available to serve on?
78
Suppose you score 88% on your midterm and score 72% on your final. Using the weights of 38% for the midterm and 62% for the final exam, find the weighted average of your scores.
78.08%
A survey taken in 2004 showed the number of American houses with more than three bedrooms. According to the survey, 4,805 of the total 10,342 houses surveyed have more than three bedrooms and 5,537 have less than or equal to 3 bedrooms. A. If a house is selected at random from the survey population, find the probability that it has more than three bedrooms. B. Find the probability that a random house has less than 4 bedrooms (AKA less than or equal to 3 bedrooms). C. Is it possible, given this information, to find the probability that a random house has exactly 2 bedrooms? D. Is it possible to find the probability that a random house has somewhere between 0 and 3 (either zero, one, two, or three) bedrooms? E. Is the number of houses with exactly one bedroom discrete or continuous? Can we determine this from the information given?
A. .4646 B. .5354 C. No, impossible. D. Yes, it's .5354, because another way of saying that is less than or equal to 3 bedrooms. E. Discrete, and yes, we can, because no matter what the exact number is, it's not going to be something like 100.03 houses, because houses themselves come in integers.
The playing life of a Sunshine radio is normally distributed with mean μ = 865 hours and standard deviation σ = 163. What is the probability that a radio selected at random will last from 865 to 1028 hours? A.0.34 B. 0.475 C. 0.4985 D. none of these
A. 0.34
Compute: BY HAND - SHOW YOUR WORK A. P7,3 B. C4,3
A. 5040/24 = 210 B. 24/6 = 4
Old Friends Information Service is a California company that is in the business of finding addresses of long-lost friends. Old Friends claims to have a 85% success rate. Suppose that you have the names of 14 friends for whom you have no addresses and decide to use Old Friends to track them. What is the expected number of friends for whom addresses will be found? What is the standard deviation? A. μ = 11.90, σ = 1.34 B. μ = 11.90, σ = 1.79 C. μ = 0.2, σ = 1.34 D. μ = 0.2, σ = 11.90
A. μ = 11.90, σ = 1.34
A local newspaper reported that approximately 76% of the people who are told that a product is improved will believe that is, in fact, improved. The remaining 24% believe that this is just hype. Suppose a marketing study consisted of a random sample of 18 people who are given a sales talk about a new, improved product. Compute the expected number of people who will believe the product is improved and the standard deviation of the resulting probability distribution. A. μ = 13.68, σ = 1.81 B. μ = 1.81, σ = 3.28 C. μ = 13.86, σ = 3.28 D. μ = 0.43, σ = 13.68
A. μ = 13.68, σ = 1.81
Mrs. Lee is the director of a student volunteer program that donates work time to various community projects. For a random sample of students in the program, Mrs. Lee found the mean was |x =505 with a standard deviation s=29. Determine a Chebyshev interval about the mean in which at least 75% of the data fall.
At least 93.8% of the students volunteered from 18.8 to 34.8 hours each semester.
In the long run, as the sample size increases and increases, the relative frequencies of ________ get closer and closer to the theoretical (or actual) probability value. Which choice best fills in the blank? A. guesses B. outcomes C. choices D. probabilities E. numbers
B
Assuming that the highest of college women are normally distributed, with a mean of 61.7 inches and standard deviation of 3.2 in., what is the percentage of women that are between 61.7 in. and 64.9 in.? A. 79% B. 34% C. 49.85% D. none of these
B. 34%
A waiter at the Green Spot Restaurant has learned, from long experience, that the probability that a lone diner will leave a tip is only 0.38. During one lunch hour he serves 8 people who are dining by themselves. Computer the mean and standard deviation of resulting distribution. A. μ = 3.04, σ = 1.88 B. μ = 3.04, σ = 1.373 C. μ = 0.851, σ = 3.04 D. μ = 1.373, σ = 1.88
B. μ = 3.04, σ = 1.373
A football team's coach predicts that his team will win 9 out of 10, or 90%, of its games. Which method did he most likely use to make this prediction? A. probability B. law of large number C. intuition D. equally likely outcomes E. relative frequency
C
Data collected over a period of years shows that the average daily temperature in Honolulu is μ = 84°F with standard deviation σ = 9°F. Convert the following interval to °F to an interval of z values. 66°F < x < 97°F A. 0.68 < z < 1.05 B. -1.14 < z < -0.77 C. -2.00 < z <1.44 D. none of these
C. -2.00 < z < 1.44
The playing life of a Sunshine radio is normally distributed with mean μ = 154 hours and standard deviation σ = 183. What is the probability that a radio selected at random will last from 154 to 703 hours? A. 0.475 B. 0.34 C. 0.4985 D. none of these
C. 0.4985
Archaeological studies have used the method of tree-ring dating in an effort to determine when prehistoric people lived in a pueblo. Wood from several excavations gave a mean of (year) 1091 with a standard deviation of 22 years. The distribution of dates was more or less mound shaped and symmetrical about the mean. Use empirical rule to estimate the range og years centered about the mean in which about 95% of the data will be found. A. 1047 to 1091 (years). B. 1046 to 1047 (years). C. 1047 and 1135 (years). D. none of these
C. 1047 and 1135 (years).
A pizza parlor franchise specifies that the average (mean) amount of cheese on a large pizza should be 5 oz and the standard deviation only 0.5 oz. An inspector picks out a large pizza at random in one of the pizza parlors and finds that it is made with 4.5 oz of cheese. Assume that the amount of cheese on a pizza follows more than three standard deviations below the mean, the parlor will be in danger of losing its franchise. How many standard deviations from the mean is 4.5? Is the pizza parlor in danger of losing its franchise? A. z = -0.80; The parlor will not lose its franchise. B. z = -0.80; The parlor will lose its franchise. C. z = -1.00; The parlor will not lose its franchise. D. none of these
C. z = -1.00; The parlor will not lose its franchise.
A recent study on prisons found that about 15% of all prison parolees become repeat offenders. Chris is a social worker whose job is to counsel people on parole. Let us say success means that a person does not become a repeat offender. Chris has been given a group of 5 parolees. What is the expected number of people who will not become repeat offenders? What is the standard deviation? (Please round your answer to two decimal places.) A. μ = 4.25, σ = 0.12 B. μ = 0.12, σ = 4.25 C. μ = 4.25, σ = 0.8 D. μ = 0.12, σ = 0.8
C. μ = 4.25, σ = 0.8
The Quick Turn Taxi Company wants to estimate the probability that a taxi will be in a wreck during a one-month period. Last month 2 out of their 200 taxis were involved in a wreck. What would you estimate the probability to be? What method did you use to get your estimate?
P=0.01; Relative frequency
Choose the word that does not complete the following statement: Statistics is the study of how to ______, _____, _____, and _____ numerical information from data. A. randomize B. analyze C. collect D. interpret E. organize
D. interpret
Compute the number of ordered seating arrangements for seven people in a car that seats five. A. 60 B. 840 C. 42 D. 5,040 E. 2,530
E
Find a positive z value such that 88.36% of the area under the standard normal curve is between -z and z. Use a table.
From the table, we can see that a z value of -1.57 corresponds to the area of 0.0582. Thus, 88.36% of the area under the standard curve is contained between -1.57 and 1.57 The positive value is 1.57.
Explain interpolation.
Interpolation is predicting y values for x values that are between x values of points in a scatter diagram.
Five balls (two red, two blue, and one yellow) are mixed up. At random, one ball is chosen and set aside, and then another ball is chosen and set aside. Are these independent? What is the probability that neither ball is blue?
No. 0.3
Find Q1, Q2, Q3, and the interquartile range of the following set of data: 1.2 3.6 5.1 4.8 10.2 6.1 7.3 9.5 2.4 11.1 0.7 1.9 4.6 2.1 9.8
Q1 = 2.1; Q2 = 4.8; Q3 = 9.5; IQR = 7.4
What does A^c mean?
The conditional probability measures the probability of an event given that another event has occurred already.
A pizza parlor franchise specifies that the average (mean) amount of cheese on a large pizza should be 10 oz and the standard deviation only 0.7 oz. The franchise specifies that the minimum amount of cheese for a large pizza is 3 standard deviations below the mean. A pizza parlor can lose its franchise if the amount of cheese on a large pizza is less than the specified minimum. What is the minimum amount of cheese, in ounces, that can be placed on a large pizza according to the franchise?
The franchise will not approve a large pizza with less than 7.9 oz of cheese.
According to Chebyshev's theorem, if |x = 200 and s = 5, what is the interval in which 88.9% of the data should fit?
They must be within 5 standard deviations of the mean. 195 to 205.
Find the indicated probability. Assume that x has a normal distribution with specified mean and standard deviation. Use a table. P(9 ≤ x ≤ 10); μ = 8, σ = 2 (Please round your answer to four decimal places.)
The probability is 0.1498
Let x have a normal distribution with μ = 49, σ = 6. Find the probability that an x value selected at random from this distribution is between 51 and 54. In symbols, find P(51 ≤ x ≤ 54). Use a table. (Please round your answer to four decimal places.)
The probability is 0.1674
Find the indicated probability. Assume that x has a normal distribution with specified mean and standard deviation. Use a table. P(53 ≤ x ≤ 59); μ = 55, σ = 5 (Please round your answer to four decimal places.)
The probability is 0.4435
True or false? The percentage of the area under a normal curve which lies to the left of μ + 2σ is 97.5%/ A. True B. False
True
Out of 1000 car-door handles tested, 23 were found to be defective. ( a) Use the probability formula for relative frequency to determine the probability that a car-door handle is defective. ( b) Using the result from part ( a), how many car-door handles out of 5,000 do you expect to be defective?
a) 0.023 b) 115 defective car-door handles
You draw one card from a standard deck of 52 cards. ( a) What is the probability that the first card is the king of diamonds and the second is the king of hearts? ( b) What is the probability that the first card is the king of diamonds and the second card is a diamond? ( c) What is the probability that the first card is not a king and the second card is also not a king?
a) P(ace of spades)= 0.0192 b) P(spade)= 0.25 c) P(ace or spade)= 0.3077
You draw two cards from a standard deck of 52 cards and do not replace the first card before you draw the second. ( a) What is the probability that the first card is the king of diamonds and the second is the king of hearts? ( b) What is the probability that the first card is the king of diamonds and the second card is a diamond? ( c) What is the probability that the first card is not a king and the second card is also not a king?
a) P((king of diamonds, king of hearts))= 0.0004 b) P((king of diamonds, diamond))= 0.0045 c) P(neither card is a king)= 0.8507
Andrea did a survey in her statistics class and found that 18 students out of 30 use the library at least twice a week. ( a) What is the probability that a student chosen at random from the class uses the library at least twice a week? ( b) What is the probability that a student chosen at random from the class uses the library less often than twice a week? ( c) If two students are chosen at random from the class what is the probability that both of them use the library at least twice a week? ( d) What is the probability that neither of them uses the library at least twice a week?
a) P(library user)= 0.6 b) P(not library user)= 0.4 c) P(2 library users) 0.3517 d) P(2 library non-users) 0.1517
In the process of tuna fishing, porpoises are sometimes accidentally caught and killed. A U.S. oceanographic institute wants to study the number of porpoises killed in this way. Records from eight commercial tuna fishing fleets gave the following information about the number of porpoises killed in a three month period: 2 6 18 9 0 15 3 10 Find the sample standard deviation.
s = 6.36
Petroleum pollution in oceans is known to increase the growth of a certain bacteria. Brain did a project for his ecology class in which he made a bacteria count (per 100 milliliters) in nine random samples of sea water. His counts gave the following readings: 17 23 18 19 21 16 12 15 18 Find the sample standard deviation.
s= 3.24
pg. 138 Figure 4.8 (in textbook) Using the least squares line, what is the value of y when x = 11. (Use data from pg. 136-138)
y = about 65
The average hours worked per week in 2001 by the eight employees of Johnson Electric are as follows. 0.48 0.79 0.56 1.09 1.12 2.24 0.98 0.87 1.69 1.98 Compute the range, population mean, and population standard deviation. A. Range = $1.75; μ = $1.18; σ = $0.57 B. Range = $1.76; μ = $1.17; σ = $0.57 C. Range = $1.76; μ = $1.18; σ = $0.57 D. Range = $1.76; μ = $1.18; σ = $0.60 E. Range = $1.77; μ = $1.18; σ = $0.60
μ = 40.23 hr; σ = 2.37 hr; 35.49 hr to 49.97 hr
