STT 315 Practice Problems I for Sections

Transcription

1 STT 35 Practice Problems I for Sections MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. ) Parking at a university has become a problem. University administrators are interested in determining the average time it takes a student to find a parking spot. An administrator inconspicuously followed 300 students and recorded how long it took each of them to find a parking spot. Identify the variable of interest to the university administration. A) number of empty parking spots B) number of students who cannot find a spot C) time to find a parking spot D) students who drive cars on campus 2) An assembly line is operating satisfactorily if fewer than 4% of the phones produced per day are defective. To check the quality of a day's production, the company randomly samples 0 phones from a day's production to test for defects. Define the population of interest to the manufacturer. A) the 0 phones sampled and tested B) the 4% of the phones that are defective C) all the phones produced during the day in question D) the 0 responses: defective or not defective 3) The manager of a car dealership records the colors of automobiles on a used car lot. Identify the type of data collected. A) qualitative B) quantitative 4) An usher records the number of unoccupied seats in a movie theater during each viewing of a film. Identify the type of data collected. A) qualitative B) quantitative 5) What number is missing from the table? ) 2) 3) 4) 5) Year in College Frequency Relative Frequency Freshman Sophomore Junior.22 Senior A) 440 B) 520 C) 480 D) 220

2 6) 6) The manager of a store conducted a customer survey to determine why customers shopped at the store. The results are shown in the figure. What proportion of customers responded that merchandise was the reason they shopped at the store? A) 2 7 B) 2 C) 3 7 D) 30 7) A survey was conducted to determine how people feel about the quality of programming available on television. Respondents were asked to rate the overall quality from 0 (no quality at all) to 00 (extremely good quality). The stem-and-leaf display of the data is shown below. 7) Stem Leaf What percentage of the respondents rated overall television quality as very good (regarded as ratings of 80 and above)? A) 3% B) 4% C) % D) 2% 8) Fill in the blank. One advantage of the is that the actual data values are retained in the graphical summarization of the data. A) stem-and-leaf plot B) pie chart C) histogram 8) 2

3 9) A sociologist recently conducted a survey of senior citizens who have net worths too high to qualify for Medicaid but have no private health insurance. The ages of the 25 uninsured senior citizens were as follows: 9) Find the median of the observations. A) 73 B) 72.5 C) 69 D) 72 0) The scores for a statistics test are as follows: 0) Compute the mean score. A) 75 B) C) D) ) At the U.S. Open Tennis Championship a statistician keeps track of every serve that a player hits during the tournament. The statistician reported that the mean serve speed of a particular player was 95 miles per hour. Suppose that the statistician indicated that the serve speed distribution was skewed to the left. Which of the following values is most likely the value of the median serve speed? A) 04 mph B) 77 mph C) 86 mph D) 95 mph ) 2) A shoe company reports the mode for the shoe sizes of men's shoes is 2. Interpret this result. 2) A) Most men have shoe sizes between and 3. B) Half of all men's shoe sizes are size 2 C) Half of the shoes sold to men are larger than a size 2 D) The most frequently occurring shoe size for men is size 2 3) Which of the following is not a measure of central tendency? 3) A) mode B) mean C) range D) median 4) Calculate the range of the following data set: 4) 9, 5, 6, 3, 6, 4, 5, 5, 6 A) 4 B) C) 7 D) 3 5) The top speeds for a sample of five new automobiles are listed below. Calculate the standard deviation of the speeds. 5) 35, 80, 55, 70, 20 A) B) C) D)

4 6) Each year advertisers spend billions of dollars purchasing commercial time on network television. In the first 6 months of one year, advertisers spent $. billion. Who were the largest spenders? In a recent article, the top 0 leading spenders and how much each spent (in million of dollars) were listed: 6) Company A $7.8 Company F $25.9 Company B 62.2 Company G 25.7 Company C 55.9 Company H 2.5 Company D 55.5 Company I 2.4 Company E 29.7 Company J 20.8 Calculate the sample variance. A) B) C) D) ) Compute s2 and s for the data set: -2, -, -3, -2, -, -4 7) A) 32.63; 5.7 B) 0.2; 0.45 C) 0.24; 0.49 D).37;.7 8) The range of scores on a statistics test was 42. The lowest score was 57. What was the highest score? A) 70.5 B) cannot be determined C) 78 D) 99 8) 9) Which of the following is a measure of the variability of a distribution? 9) A) median B) sample size C) range D) skewness 20) The temperature fluctuated between a low of 73 F and a high of 89 F. Which of the following could be calculated using just this information? A) median B) standard deviation C) range D) variance 20) Answer the question True or False. 2) A larger standard deviation means greater variability in the data. 2) A) True B) False Solve the problem. 22) The total points scored by a basketball team for each game during its last season have been summarized in the table below. Which statement following the table must be true? 22) Score Frequency A) The range is at least 4 but at most 79. B) The range is at least 4 but at most 20. C) The range is 79. D) The range is at least 8 but at most ) The mean x of a data set is 36.7, and the sample standard deviation s is Find the interval representing measurements within one standard deviation of the mean. A) (35.7, 37.7) B) (33.49, 39.93) C) (27.05, 46.37) D) (30.27, 43.5) 23) 4

5 24) The following is a list of 25 measurements: 24) How many of the measurements fall within one standard deviation of the mean? A) 3 B) 6 C) 25 D) 8 25) A standardized test has a mean score of 500 points with a standard deviation of 00 points. Five students' scores are shown below. 25) Adam: 575 Beth: 690 Carlos: 750 Doug: 280 Ella: 440 Which of the students have scores within two standard deviations of the mean? A) Adam, Beth B) Carlos, Doug C) Adam, Beth, Carlos, Ella D) Adam, Beth, Ella 26) A study was designed to investigate the effects of two variables () a student's level of mathematical anxiety and (2) teaching method on a student's achievement in a mathematics course. Students who had a low level of mathematical anxiety were taught using the traditional expository method. These students obtained a mean score of 490 with a standard deviation of 40 on a standardized test. Assuming a mound-shaped and symmetric distribution, what percentage of scores exceeded 40? A) approximately 97.5% B) approximately 95% C) approximately 84% D) approximately 00% 27) A study was designed to investigate the effects of two variables () a student's level of mathematical anxiety and (2) teaching method on a student's achievement in a mathematics course. Students who had a low level of mathematical anxiety were taught using the traditional expository method. These students obtained a mean score of 420 with a standard deviation of 20 on a standardized test. Assuming a mound-shaped and symmetric distribution, in what range would approximately 99.7% of the students score? A) below 480 B) below 360 and above 480 C) between 360 and 480 D) above ) A study was designed to investigate the effects of two variables () a student's level of mathematical anxiety and (2) teaching method on a student's achievement in a mathematics course. Students who had a low level of mathematical anxiety were taught using the traditional expository method. These students obtained a mean score of 430 with a standard deviation of 20 on a standardized test. Assuming no information concerning the shape of the distribution is known, what percentage of the students scored between 390 and 470? A) at least 75% B) approximately 68% C) at least 89% D) approximately 95% 26) 27) 28) 5

6 29) By law, a box of cereal labeled as containing 20 ounces must contain at least 20 ounces of cereal. The machine filling the boxes produces a distribution of fill weights with a mean equal to the setting on the machine and with a standard deviation equal to 0.03 ounce. To ensure that most of the boxes contain at least 20 ounces, the machine is set so that the mean fill per box is ounces. Assuming nothing is known about the shape of the distribution, what can be said about the proportion of cereal boxes that contain less than 20 ounces. A) The proportion is at most %. B) The proportion is less than 2.5%. C) The proportion is at most 5.5%. D) The proportion is at least 89%. 30) If nothing is known about the shape of a distribution, what percentage of the observations fall within 2 standard deviations of the mean? A) approximately 95% B) at least 75% C) at most 25% D) approximately 5% 29) 30) 3) Which of the following is a measure of relative standing? 3) A) mean B) z-score C) variance D) pie chart 32) Many firms use on-the-job training to teach their employees computer programming. Suppose you work in the personnel department of a firm that just finished training a group of its employees to program, and you have been requested to review the performance of one of the trainees on the final test that was given to all trainees. The mean and standard deviation of the test scores are 79 and 2, respectively, and the distribution of scores is mound-shaped and symmetric. Suppose the trainee in question received a score of 72. Compute the trainee's z-score. A) z = -4 B) z = -7 C) z = 0.89 D) z = ) Summary information is given for the weights (in pounds) of 000 randomly sampled tractor trailers. 32) 33) MIN: %: 5605 MAX: 0,605 75%: 8605 AVE: 7005 Std. Dev.: 400 Find the percentage of tractor trailers with weights between 5605 and 8605 pounds. A) 25% B) 75% C) 50% D) 00% 34) When Scholastic Achievement Test scores (SATs) are sent to test-takers, the percentiles associated with scores are also given. Suppose a test-taker scored at the 66th percentile on the verbal part of the test and at the 45th percentile on the quantitative part. Interpret these results. A) This student performed better than 34% of the other test-takers on the verbal part and better than 55% on the quantitative part. B) This student performed better than 66% of the other test-takers on the verbal part and better than 55% on the quantitative part. C) This student performed better than 34% of the other test-takers on the verbal part and better than 45% on the quantitative part. D) This student performed better than 66% of the other test-takers on the verbal part and better than 45% on the quantitative part. 34) Answer the question True or False. 35) The mean of a data set is at the 50th percentile. 35) A) True B) False 6

7 Solve the problem. 36) At the U.S. Open Tennis Championship a statistician keeps track of every serve that a player hits during the tournament. The statistician reported that the mean serve speed of a particular player was 02 miles per hour (mph) and the standard deviation of the serve speeds was 4 mph. Using the z-score approach for detecting outliers, which of the following serve speeds would represent outliers in the distribution of the player's serve speeds? 36) Speeds: 53 mph, 6 mph, and 30 mph A) 53, 6, and 30 are all outliers. B) 53 is the only outlier. C) 53 and 6 are both outliers, but 30 is not. D) None of the three speeds is an outlier. 37) A sociologist recently conducted a survey of citizens over 60 years of age who have net worths too high to qualify for Medicaid but have no private health insurance. The ages of the 25 uninsured senior citizens were as follows: 37) Find the upper quartile of the data. A) 92 B) 65.5 C) 73 D) ) At the U.S. Open Tennis Championship a statistician keeps track of every serve that a player hits during the tournament. The lower quartile of a particular player's serve speeds was reported to be 88 mph. Which of the following interpretations of this information is correct? A) 75% of the player's serves were hit at speeds greater than 88 mph. B) 88 serves traveled faster than the lower quartile. C) 75% of the player's serves were hit at speeds less than 88 mph. D) 25% of the player's serves were hit at 88 mph. 39) The box plot shown below displays the amount of soda that was poured by a filling machine into 2-ounce soda cans at a local bottling company. 38) 39) Based on the box plot, what shape do you believe the distribution of the data to have? A) skewed to the center B) skewed to the right C) approximately symmetric D) skewed to the left 7

8 40) If sample points A, B, C, and D are the only possible outcomes of an experiment, find the probability of D using the table below. 40) Sample Point A B C D Probability A) 3 8 B) 5 8 C) 4 D) 8 4) The outcome of an experiment is the number of resulting heads when a nickel and a dime are flipped simultaneously. What is the sample space for this experiment? A) {HH, HT, TH, TT} B) {0,, 2} C) {HH, HT, TT} D) {nickel, dime} 42) A bag of colored candies contains 20 red, 25 yellow, and 35 orange candies. An experiment consists of randomly choosing one candy from the bag and recording its color. What is the sample space for this experiment? A) 4, 5 6, 7 B) {80} 6 4) 42) C) {red, yellow, orange} D) {20, 25, 35} 43) An experiment consists of randomly choosing a number between and 0. Let E be the event that the number chosen is even. List the sample points in E. A) {2, 4, 6, 8, 0} B) {, 3, 5, 7, 9} C) {5} D) {, 2, 3, 4, 5, 6, 7, 8, 9, 0} 44) Probabilities of different types of vehicle-to-vehicle accidents are shown below: 43) 44) Accident Probability Car to Car 0.65 Car to Truck 0.7 Truck to Truck 0.8 Find the probability that an accident involves a car. A) 0.8 B) 0.7 C) 0.65 D) ) At a community college with 500 students, 20 students are age 30 or older. Find the probability that a randomly selected student is age 30 or older. A).76 B).2 C).24 D).30 46) A clothing vendor estimates that 78 out of every 00 of its online customers do not live within 50 miles of one of its physical stores. Using this estimate, what is the probability that a randomly selected online customer does not live within 50 miles of a physical store? A).22 B).28 C).50 D).78 45) 46) 8

9 47) At a certain university, one out of every 20 students is enrolled in a statistics course. If one student at the university is chosen at random, what is the probability that the student is enrolled in a statistics course? A) 2 B) 20 C) 2 D) 9 47) 48) Two chips are drawn at random and without replacement from a bag containing four blue chips and three red chips. Find the probability of drawing two red chips. A) B) 6 9 C) D) ) 49) A pair of fair dice is tossed. Events A and B are defined as follows. 49) A: {The sum of the numbers on the dice is 3} B: {At least one of the dice shows a 2} Identify the sample points in the event A B. A) {(, 2), (2, ), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)} B) {(, 2), (2, )} C) {(2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (4, 2), (5, 2), (6, 2)} D) {(, 2), (2, ), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (4, 2), (5, 2), (6, 2)} 50) Consider the Venn diagram below where P(E) = P(E2) = 5, P(E 3) = P(E4) = P(E5) = 0, 50) P(E6) = P(E7) = 20, and P(E 8) =. Find P(A B). 5 A) 3 5 B) C) 2 D) 2 5 9

10 5) Consider the Venn diagram below where P(E) = 0., P(E2) = 0.2, P(E3) = 0.03, P(E4) = 0.06, P(E5) = 0.06, P(E6) = 0., P(E7) = 0.06, P(E8) = 0.08, and P(E9) = 0.3. Find P(A B). 5) A) B) 0.26 C) 0.69 D) ) A state energy agency mailed questionnaires on energy conservation to,000 homeowners in the state capital. Five hundred questionnaires were returned. Suppose an experiment consists of randomly selecting one of the returned questionnaires. Consider the events: 52) A: {The home is constructed of brick} B: {The home is more than 30 years old} In terms of A and B, describe a home that is constructed of brick and is less than or equal to 30 years old. A) A Bc B) A B C) (A B)c D) A B 53) A state energy agency mailed questionnaires on energy conservation to,000 homeowners in the state capital. Five hundred questionnaires were returned. Suppose an experiment consists of randomly selecting one of the returned questionnaires. Consider the events: 53) A: {The home is constructed of brick} B: {The home is more than 30 years old} D: {The home is heated with oil} Which of the following describes the event B Dc? A) homes that are not older than 30 years old and heated with oil B) homes more than 30 years old that are heated with oil C) homes more than 30 years old or homes that are not heated with oil D) homes more than 30 years old that are not heated with oil 0

11 54) Consider the Venn diagram below where P(E) = 0., P(E2) = 0.2, P(E3) = 0.03, P(E4) = 0.04, P(E5) = 0.07, P(E6) = 0., P(E7) = 0.07, P(E8) = 0.07, and P(E9) = Find P(Bc). 54) A) 0.66 B) 0.2 C) 0.56 D) ) Consider the Venn diagram below where P(E) = 0., P(E2) = 0.2, P(E3) = 0.05, P(E4) = 0.06, P(E5) = 0.06, P(E6) = 0., P(E7) = 0.06, P(E8) = 0.03, and P(E9) = Find P(Ac B). 55) A) 0.26 B) 0.78 C) 0.52 D) 0.8 Answer the question True or False. 56) An event and its complement are mutually exclusive. 56) A) True B) False Solve the problem. 57) If P(A B) = and P(A B) = 0, then which statement is true? 57) A) A and B are complementary events. B) A and B are reciprocal events. C) A and B are both empty events. D) A and B are supplementary events. Answer the question True or False. 58) If events A and B are not mutually exclusive, then it is possible that P(A) + P(B) >. 58) A) True B) False

12 Solve the problem. 59) Suppose that for a certain experiment P(A) =.33 and P(B) =.29. If A and B are mutually exclusive events, find P(A B). A).38 B).62 C).03 D).3 59) 60) Suppose that for a certain experiment P(A) =.47 and P(B) =.25 and P(A B) =.4. Find P(A B). 60) A).86 B).36 C).72 D).58 6) Four hundred accidents that occurred on a Saturday night were analyzed. The number of vehicles involved and whether alcohol played a role in the accident were recorded. The results are shown below: 6) Number of Vehicles Involved Did Alcohol Play a Role? 2 3 or more Totals Yes No Totals Suppose that one of the 400 accidents is chosen at random. What is the probability that the accident involved alcohol or a single car? A) 7 B) C) D) ) In a class of 40 students, 22 are women, 0 are earning an A, and 7 are women that are earning an A. If a student is randomly selected from the class, find the probability that the student is a woman given that the student is earning an A. A) 20 B) 7 22 C) 7 0 D) 5 62) 63) Four hundred accidents that occurred on a Saturday night were analyzed. The number of vehicles involved and whether alcohol played a role in the accident were recorded. The results are shown below: 63) Number of Vehicles Involved Did Alcohol Play a Role? 2 3 or more Totals Yes No Totals Given that an accident involved multiple vehicles, what is the probability that it involved alcohol? A) B) C) D) ) For two events, A and B, P(A) =.4, P(B) =.7, and P(A B) =.2. Find P(A B). 64) A).29 B).4 C).08 D).5 65) For two events, A and B, P(A) =.6, P(B) =.8, and P(A B) =.5. Find P(A B). 65) A).4 B).3 C).833 D).625 2

13 66) Suppose that for a certain experiment P(B) =.5 and P(A B) =.2. Find P(A B). 66) A).3 B). C).4 D).7 67) Suppose that for a certain experiment P(A) =.6 and P(B) =.3. If A and B are independent events, find P(A B). A).8 B).90 C).50 D).30 68) A study revealed that 45% of college freshmen are male and that 8% of male freshmen earned college credits while still in high school. Find the probability that a randomly chosen college freshman will be male and have earned college credits while still in high school. A).400 B).08 C).530 D) ) A number between and 0, inclusive, is randomly chosen. Events A, B, C, and D are defined as follows. 67) 68) 69) A: {The number is even} B: {The number is less than 7} C: {The number is less than or equal to 7} D: {The number is 5} Identify one pair of independent events. A) A and B B) A and D C) A and C D) B and D 70) Classify the events as dependent or independent: Events A and B where P(A) = 0.2, P(B) = 0., and P(A and B) = A) dependent B) independent 7) From 9 names on a list, a sample of 4 will be asked about voting preferences in an upcoming election. How many different samples are possible? A) 3024 B) 52 C) 5,20 D) 26 70) 7) 72) Which expression is equal to N n? 72) A) N! (N - n)! B) N! N!(N - n)! C) N! n! D) N! n!(n - n)! 73) Kim submitted a list of 2 movies to an online movie rental company. The company will choose 3 of the movies and ship them to her. If all movies are equally likely to be chosen, what is the probability that Kim will receive the three movies that she most wants to watch? A) 220 B) 728 C) 320 D) 4 73) 74) Suppose that B and B2 are mutually exclusive and complementary events, such that P(B) =.6 and P(B2) =.4. Consider another event A such that P(A B) =.2 and P(A B2) =.5. Find P(A). A).32 B).70 C).88 D).38 75) Suppose that B and B2 are mutually exclusive and complementary events, such that P(B) =.6 and P(B2) =.4. Consider another event A such that P(A B) =.2 and P(A B2) =.5. Find P(B A). A).375 B).800 C).625 D) ) 75) 3

14 76) 2.5% of a population are infected with a certain disease. There is a test for the disease, however the test is not completely accurate. 94.9% of those who have the disease will test positive. However 4.5% of those who do not have the disease will also test positive (false positives). What is the probability that a person who tests positive actually has the disease? A) B) C) D) 0.54 E) ) In the town of Maplewood a certain type of DVD player is sold at just two stores. 42% of the sales are from store A and 58% of the sales are from store B. 2.3% of the DVD players sold at store A are defective while 3.7% of the DVD players sold at store B are defective. If Kate receives one of these DVD players as a gift and finds that it is defective, what is the probability that it came from store A? A) B) 0.42 C) D) E) ) 77) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. 78) For a given data set, the lower quartile is 45, the median is 50, and the upper quartile is 57. The minimum value in the data set is 32, and the maximum is 8. 78) a. Find the interquartile range. b. Find the inner fences. c. Find the outer fences. d. Is either of the minimum or maximum values considered an outlier? Explain. 79) The calculator screens summarize a data set. 79) a. Identify the lower and upper quartiles of the data set. b. Find the interquartile range. c. Is there reason to suspect that the data may contain an outlier? Explain. 80) Use a graphing calculator or software to construct a box plot for the following data set. 80) ) Suppose that an experiment has five sample points, E, E2, E3, E4, E5, and that P(E) = 0.2, P(E2) = 0.3, P(E3) = 0., P(E4) = 0., and P(E5) = 0.3. If the events A and B are defined as A = {E, E2, E3} and B = {E2, E3, E4}, find P(A B). 8) 82) Suppose that for a certain experiment P(A) =.37. Find P(Ac). 82) 4

15 83) Two chips are drawn at random and without replacement from a bag containing two blue chips and two red chips. Event A is defined as follows. 83) A: {Both chips are red} a. Describe the event Ac. b. Identify the sample points in the event Ac. c. Find P(Ac). 84) Suppose there is a 36% chance that a risky stock investment will end up in a total loss of your investment. Because the rewards are so high, you decide to invest in three independent risky stocks. What is the probability that all three stocks end up in total losses? 84) 5

16 STT 35 Practice Test - ANSWERS ) C 2) C 3) A 4) B 5) A 6) C 7) B 8) A 9) D 0) B ) A 2) D 3) C 4) B 5) B 6) B 7) D 8) D 9) C 20) C 2) A 22) A 23) B 24) B 25) D 26) A 27) C 28) A 29) A 30) B 3) B 32) D 33) C 34) D 35) B 36) B 37) D 38) A 39) D 40) B 4) B 42) C 43) A 44) D 45) C 46) D 47) B 48) A 49) D 50) C 5) C 52) A 53) C 54) C 55) D 56) A 57) A 58) A 59) B 60) D 6) B 62) C 63) D 64) A 65) A 66) B 67) A 68) B 69) A 70) B 7) D 72) D 73) A 74) A 75) A 76) E 77) E 78) a. The interquartile range is = 2. b. The inner fences are (2) = 27 and (2) = 75. c. The outer fences are 45-3(2) = 9 and (2) = 93. d. The maximum of 8 is a potential outlier since it lies outside the inner fences. The minimum is within the inner fence and is not considered to be an outlier. 79) a. lower quartile: Q=75; upper quartile: Q3=90 b. interquartile range: = 5 c. Yes; the smallest measurement, 30, is three times the interquartile range less than the lower quartile, so it is a suspected outlier. 80) The horizontal axis extends from 0 to 20, with each tick mark representing one unit.

17 8) A B = {, }; P(A B) = P( ) + P( ) = = ) P(Ac) = =.63 83) a. At least one chip is not red. b. {bb2, br, br2, b2r, b2r2} c. P(Ac) =5/6 84) Let be the event that stock i ends up in a total loss. P(all three stocks end in total loss) = P( ) = P( ) P( ) P( ) = = 0.047