AP Statistics Practice ExamTopic-Based Review20251 Probability: General Rules, Independence, and Conditional Probability1. A high school science teacher has 78 students. Of those students, 35 are in the band and 32 are on asports team. There are 16 students who are not in the band or on a sports team. One student from the78 students will be selected at random. Let event B represent the event of selecting a student in theband, and let event S represent the event of selecting a student on a sports team. Are B and S mutuallyexclusive events?A. No, because P(B intersect S) = 5/78.B. No, because P(B intersect S) = 48/78.C. No, because P(B intersect S) = 62/78.D. Yes, because P(B intersect S) = 5/78.E. Yes, because P(B intersect S) = 62/78.TeamHome Away Total2. Purchased food 120 40 160Did not purchase food 60 30 90Total 180 70 250The table shows data that were collected from people who attended a certain high school basketballgame. A person who attended the game will be selected at random. Which of the following correctlyinterprets mutually exclusive events represented by the table?A. Rooting for the home team and rooting for the away teamB. Rooting for the home team and purchasing food during the gameC. Rooting for the away team and purchasing food during the gameD. Rooting for the home team and not purchasing food during the gameE. Not rooting for the home team and not purchasing food during the game3. A middle school chess club has 5 members: Adam, Bradley, Carol, Dave, and Ella. Two studentsfrom the club will be selected at random to participate in the county chess tournament. What is theprobability that Adam and Ella will be selected?A. 1/20B. 1/10C. 1/8D. 1/7E. 1/54. Events D and E are independent, with P(D) = 0.6 and P(D and E) = 0.18. Which of the following istrue?1A. P(E) = 0.12B. P(E) = 0.4C. P(D or E) = 0.28D. P(D or E) = 0.72E. P(D or E) = 0.95. One student from a high school will be selected at random. Let A be the event that the selected studentis a student athlete, and let B be the event that the selected student drives to school. If P(A intersect B) = 0.08and P(B|A) = 0.25, what is the probability that the selected student will be a student athlete?A. 0.02B. 0.17C. 0.32D. 0.33E. 3.136. Each of the faces of a fair six-sided number cube is numbered with one of the numbers 1 through 6, witha different number appearing on each face. Two such number cubes will be tossed, and the sum of thenumbers appearing on the faces that land up will be recorded. What is the probability that the sumwill be 4, given that the sum is less than or equal to 6?A. 2/36B. 3/36C. 3/15D. 2/9E. 4/67. As a promotion, the first 50 customers who entered a certain store at a mall were asked to choose fromone of two discounts. The first discount choice was 20% off all purchases made that day. The seconddiscount choice was 10% off all purchases for the week. Of those who received the discounts, 28 chosethe first discount and 22 chose the second discount. One customer will be selected at random from thosewho received a discount. Let F represent the event that the selected person chose the first discount,and let S represent the event that the selected person chose the second discount. Are F and S mutuallyexclusive events?A. Yes, because P(F intersect S) = 0.B. Yes, because P(F intersect S) = 0.12.C. Yes, because P(F intersect S) = 1.D. No, because P(F intersect S) = 0.E. No, because P(F intersect S) = 1.8. For flights from a particular airport in January, there is a 30 percent chance of a flight being delayedbecause of icy weather. If a flight is delayed because of icy weather, there is a 10 percent chance theflight will also be delayed because of a mechanical problem. If a flight is not delayed because of icyweather, there is a 5 percent chance that it will be delayed because of a mechanical problem. If oneflight is selected at random from the airport in January, what is the probability that the flight selectedwill have at least one of the two types of delays?A. 0.065B. 0.335C. 0.350D. 0.450Page 2E. 0.6659. Ali surveyed 200 students at a school and recorded the eye color and the gender of each student. Of the80 male students who were surveyed, 60 had brown eyes. If eye color and gender are independent, howmany female students surveyed would be expected to have brown eyes?A. 5B. 20C. 30D. 90E. 10010. The SC Electric Company has bid on two electrical wiring jobs. The owner of the company believes that• the probability of being awarded the first job (event A) is 0.75;• the probability of being awarded the second job (event B) is 0.5; and• the probability of being awarded both jobs (event (A and B)) is 0.375.If the owner's beliefs are correct, which of the following statements must be true concerning event A andevent B?A. Event A and event B are mutually exclusive and are independent.B. Event A and event B are mutually exclusive and are not independent.C. Event A and event B are not mutually exclusive and are independent.D. Event A and event B are not mutually exclusive and are not independent.E. Event A and event B are not mutually exclusive, and independence cannot be determined.11. For which of the following probability assignments are events A and B independent?A. P(A intersect B^C) = 0.3, P(A intersect B) = 0.12, and P(A^C intersect B) = 0.4.B. P(A intersect B) = 0.3, P(A intersect B) = 0.3, and P(A intersect B) = 0.3.C. P(A intersect B) = 0.1, P(A intersect B) = 0.1, and P(A intersect B) = 0.4.D. P(A intersect B) = 0.3, P(A intersect B) = 0.0, and P(A intersect B) = 0.2.E. P(A intersect B^C) = 0.5, P(A intersect B) = 0.1, and P(A intersect B) = 0.4.12. Ms. Tucker travels through two intersections with traffic lights as she drives to the market. The trafficlights operate independently. The probability that both lights will be red when she reaches them is 0.22.The probability that the first light will be red and the second light will not be red is 0.33. What is theprobability that the second light will be red when she reaches it?A. 0.40B. 0.45C. 0.50D. 0.55E. 0.6013. In a certain school, 17 percent of the students are enrolled in a psychology course, 28 percent areenrolled in a foreign language course, and 32 percent are enrolled in either a psychology course or aforeign language course or both. What is the probability that a student chosen at random from thisschool will be enrolled in both a foreign language course and a psychology course?A. 0.45B. 0.32C. 0.20Page 3D. 0.13E. 0.0514. The probability that a new microwave oven will stop working in less than 2 years is 0.05. The probabilitythat a new microwave oven is damaged during delivery and stops working in less than 2 years is 0.04. Theprobability that a new microwave oven is damaged during delivery is 0.10. Given that a new microwaveoven is damaged during delivery, what is the probability that it stops working in less than 2 years?A. 0.05B. 0.06C. 0.10D. 0.40E. 0.5015. A student is applying to two different agencies for scholarships. Based on the student's academic record,the probability that the student will be awarded a scholarship from Agency A is 0.55 and the probabilitythat the student will be awarded a scholarship from Agency B is 0.40. Furthermore, if the student isawarded a scholarship from Agency A, the probability that the student will be awarded a scholarshipfrom Agency B is 0.60. What is the probability that the student will be awarded at least one of the twoscholarships?A. 0.60B. 0.62C. 0.71D. 0.73E. 0.952 Discrete Random Variables1. The following table shows the probability distribution for the number of books a student typically buysat the annual book fair held at an elementary school.Number of Books 0 1 2 3 4 5 6 7Probability 0.35 0.20 0.15 0.10 0.07 0.08 0.04 0.01Let the random variable B represent the number of books a student buys at the next book fair. Whatis the expected value of B?A. 0B. 1.00C. 1.79D. 3.50E. 282. At a large regional collegiate women's swim meet, an official records the time it takes each swimmer toswim 100 meters for all swimmers who compete in only one stroke category. The following table shows the mean times and corresponding standard deviations for the collegiate women at the swim meet foreach of the four stroke categories.Stroke Category Mean 100 meter Time Standard DeviationBackstroke 55.6 seconds 0.70 secondsBreaststroke 63.3 seconds 0.92 secondsButterfly 54.4 seconds 0.94 secondsFreestyle 50.2 seconds 0.76 secondsPage 4For each of the 4 stroke categories, consider a random variable representing the time of a randomlyselected swimmer in that category. What is the standard deviation of the sum of the 4 random variables?A. 0.83 secondsB. 1.67 secondsC. 2.80 secondsD. 3.32 secondsE. 3.76 seconds3. A player pays $15 to play a game in which a chip is randomly selected from a bag of chips. The bagcontains 10 red chips, 4 blue chips, and 6 yellow chips. The player wins $5 if a red chip is selected, $10if a blue chip is selected, and $20 if a yellow chip is selected. Let the random variable X represent theamount won from the selection of the chip, and let the random variable W represent the total amountwon, where W = X – 15. What is the mean of W?A. $10.50B. $4.50C. -$4.50D. -$6.50E. -$10.504. A city department of transportation studied traffic congestion on a certain highway. To encouragecarpooling, the department will recommend a carpool lane if the average number of people in passenger cars on the highway is less than 2. The probability distribution of the number of people in passenger cars on the highway is shown in the table.Number of people 1 2 3 4 5Probability 0.56 0.28 0.08 0.06 0.02Based on the probability distribution, what is the mean number of people in passenger cars on thehighway?A. 0.28B. 0.56C. 1.7D. 2E. 35. Every Thursday, Matt and Dave's Video Venture has "roll-the-dice" day. A customer may choose to rolltwo fair dice and rent a second movie for an amount (in cents) equal to the numbers uppermost on thedice, with the larger number first. Let X represent the amount paid for a second movie on roll-the-diceday. The expected value of X is $0.47 and the standard deviation of X is $0.15. If a customer rollsthe dice and rents a second movie every Thursday for 30 consecutive weeks, what is the approximateprobability that the total amount paid for these second movies will exceed $15.00?A. 0B. 0.09C. 0.14D. 0.86E. 0.916. The distribution of random variable R has mean 10 and standard deviation 4. The distribution ofrandom variable S has mean 7 and standard deviation 3. If R and S are independent, what are themean and standard deviation of the distribution of R - S?Page 5A. Mean 3 and standard deviation 1B. Mean 3 and standard deviation 5C. Mean 3 and standard deviation 7D. Mean 17 and standard deviation 1E. Mean 17 and standard deviation 57. At a certain bakery, the price of each doughnut is $1.50. Let the random variable D represent thenumber of doughnuts a typical customer purchases each day. The expected value and variance of theprobability distribution of D are 2.6 doughnuts and 3.6 (doughnuts)^2, respectively. Let the randomvariable P represent the price of the doughnuts that a typical customer purchases each day. Which ofthe following is the standard deviation, in dollars, of the probability distribution of P?A. 1.5(3.6)B. 1.5 sqrt(3.6)C. sqrt(1.5)(3.6)D. 1.5(2.6)E. 1.5/2.68. The XYZ Office Supplies Company sells calculators in bulk at wholesale prices, as well as individuallyat retail prices. The following tables are estimates for next year's sales.WHOLESALE SALESNumber Sold 2,000 5,000 10,000 20,000Probability 0.1 0.3 0.4 0.2RETAIL SALESNumber Sold 600 1,000 1,500Probability 0.4 0.5 0.1What profit does XYZ Office Supplies Company expect to make for the next year if the profit from eachcalculator sold is $20 at wholesale and $30 at retail?A. $10,590B. $220,700C. $264,750D. $833,100E. $1,002,5009. In a certain game, a fair die is rolled and a player gains 20 points if the die shows a "6." If the die doesnot show a "6," the player loses 3 points. If the die were to be rolled 100 times, what would be theexpected total gain or loss for the player?A. A gain of about 1,700 pointsB. A gain of about 583 pointsC. A gain of about 83 pointsD. A loss of about 250 pointsE. A loss of about 300 points10. A box contains 10 tags, numbered 1 through 10, with a different number on each tag. A second boxcontains 8 tags, numbered 20 through 27, with a different number on each tag. One tag is drawn atrandom from each box. What is the expected value of the sum of the numbers on the two selected tags?A. 13.5Page 6B. 14.5C. 15.0D. 27.0E. 29.011. Let X represent the number on the face that lands up when a fair six-sided number cube is tossed. Theexpected value of X is 3.5, and the standard deviation of X is approximately 1.708. Two fair six-sidednumber cubes will be tossed, and the numbers appearing on the faces that land up will be added. Whichof the following values is closest to the standard deviation of the resulting sum?A. 1.708B. 1.848C. 2.415D. 3.416E. 5.83512. A company that makes fleece clothing uses fleece produced from two farms, Northern Farm and WesternFarm. Let the random variable X represent the weight of fleece produced by a sheep from NorthernFarm. The distribution of X has mean 14.1 pounds and standard deviation 1.3 pounds. Let the randomvariable Y represent the weight of fleece produced by a sheep from Western Farm. The distribution ofY has mean 6.7 pounds and standard deviation 0.5 pound. Assume X and Y are independent. Let Wequal the total weight of fleece from 10 randomly selected sheep from Northern Farm and 15 randomlyselected sheep from Western Farm. Which of the following is the standard deviation, in pounds, of W?A. 1.3 +0.5B. sqrt(1.3^2 + 0.5^2)C. sqrt(10(1.3)^2 + 15(0.5)^2)D. 10^2(1.3)^2 + 15^2(0.5)^2E. 1.3^2/10 + 0.5^2/153 The Normal Distribution1. Two college roommates have each committed to donating to charity each week for the next year. Theroommates' weekly incomes are independent of each other. Suppose the amount donated in a week by oneroommate is approximately normal with mean $30 and standard deviation $10, and the amount donatedin a week by the other roommate is approximately normal with mean $60 and standard deviation $20.Which of the following is closest to the expected number of weeks in a 52-week year that their combineddonation will exceed $120?A. 0; the combined donation never exceeds $120 in a weekB. 1 weekC. 3 weeksD. 5 weeksE. 8 weeks2. The distribution of random variable R has mean 10 and standard deviation 4. The distribution ofrandom variable S has mean 7 and standard deviation 3. If R and S are independent, what are themean and standard deviation of the distribution of R - S?A. Mean 3 and standard deviation 1B. Mean 3 and standard deviation 5Page 7C. Mean 3 and standard deviation 7D. Mean 17 and standard deviation 1E. Mean 17 and standard deviation 53. A summer resort rents rowboats to customers but does not allow more than four people to a boat. Eachboat is designed to hold no more than 800 pounds. Suppose the distribution of adult males who rentboats, including their clothes and gear, is normal with a mean of 190 pounds and standard deviation of10 pounds. If the weights of individual passengers are independent, what is the probability that a groupof four adult male passengers will exceed the acceptable weight limit of 800 pounds?A. 0.023B. 0.046C. 0.159D. 0.317E. 0.9774. Carly commutes to work, and her commute time is dependent on the weather. When the weatheris good, the distribution of her commute times is approximately normal with mean 20 minutes andstandard deviation 2 minutes. When the weather is not good, the distribution of her commute times isapproximately normal with mean 30 minutes and standard deviation 4 minutes. Suppose the probabilitythat the weather will be good tomorrow is 0.9. Which of the following is closest to the probability thatCarly's commute time tomorrow will be greater than 25 minutes?A. 0.0056B. 0.0894C. 0.0950D. 0.8055E. 0.90065. Sean and Evan are college roommates who have part-time jobs as servers in restaurants. The distributionof Sean's weekly income is approximately normal with mean $225 and standard deviation $25. Thedistribution of Evan's weekly income is approximately normal with mean $240 and standard deviation$15. Assuming their weekly incomes are independent of each other, which of the following is closest tothe probability that Sean will have a greater income than Evan in a randomly selected week?A. 0.067B. 0.159C. 0.227D. 0.303E. 0.3546. A company ships gift baskets that contain apples and pears. The distributions of weight for the apples,the pears, and the baskets are each approximately normal. The mean and standard deviation for eachdistribution is shown in the table below. The weights of the items are assumed to be independent.Item Mean Standard DeviationApple 4.72 ounces 0.20 ouncePear 5.41 ounces 0.18 ounceBasket 13.25 ounces 1.88 ouncesLet the random variable W represent the total weight of 4 apples, 6 pears, and 1 basket. Which of thefollowing is closest to the standard deviation of W?A. 1.90 ouncesPage 8B. 1.97 ouncesC. 2.26 ouncesD. 3.76 ouncesE. 3.83 ounces7. The Attila Barbell Company makes bars for weight lifting. The weights of the bars are independentand are normally distributed with a mean of 720 ounces (45 pounds) and a standard deviation of 4ounces. The bars are shipped 10 in a box to the retailers. The weights of the empty boxes are normallydistributed with a mean of 320 ounces and a standard deviation of 8 ounces. The weights of the boxesfilled with 10 bars are expected to be normally distributed with a mean of 7,520 ounces and a standarddeviation ofA. sqrt(12) ouncesB. sqrt(80) ouncesC. sqrt(224) ouncesD. 48 ouncesE. sqrt(1,664) ounces8. The continuous random variable N has a normal distribution with mean 7.5 and standard deviation 2.5.For which of the following is the probability equal to 0?A. P(N = 8)B. P(N > 8)C. P(N < 8)D. P(7 < N < 8)E. P(N < 7) or P(N > 8)4 Binomial and Geometric Distributions1. A large store has a customer service department where customers can go to ask for help with store-relatedissues. According to store records, approximately 1/4 of all customers who go to the service departmentask for help finding an item. Assume the reason each customer goes to the service department isindependent from customer to customer. Based on the approximation, what is the probability that atleast 1 of the next 4 customers who go to the service department will ask for help finding an item?A. 4(1/4)B. 1- (1/4)^4C. 1-(3/4)^4D. 4(1/4)(3/4)^3E. (3/4)(3/4)(3/4)(1/4)2. Based on his past record, Luke, an archer for a college archery team, has a probability of 0.90 of hittingthe inner ring of the target with a shot of the arrow. Assume that in one practice Luke will attempt5 shots of the arrow and that each shot is independent from the others. Let the random variable Xrepresent the number of times he hits the inner ring of the target in 5 attempts. What is the probabilitythat the number of times Luke will hit the inner ring of the target out of the 5 attempts is less than themean of X?A. 0.40951B. 0.50000C. 0.59049Page 9D. 0.91854E. 0.991443. Mateo plays on his school basketball team. From past history, he knows that his probability of making abasket on a free throw is 0.8. Suppose he wants to create a simulation using random numbers to estimatethe probability of making at least 3 baskets on his next 5 free throw attempts. Which of the followingassignments of the digits 0 to 9 could be used for the simulation?A. Let the even digits represent making a basket and the odd digits represent not making a basket.B. Let the digits 0 and 1 represent making a basket and the digits from 2 to 9 represent notmaking a basket.C. Let the digits from 0 to 3 represent making a basket and the digits from 4 to 9 represent notmaking a basket.D. Let the digits from 0 to 6 represent making a basket and the digits from 7 to 9 represent notmaking a basket.E. Let the digits from 0 to 7 represent making a basket and the digits 8 and 9 represent notmaking a basket.4. According to a recent survey, 31 percent of the residents of a certain state who are age 25 years or olderhave a bachelor's degree. A random sample of 50 residents of the state, age 25 years or older, will beselected. Let the random variable B represent the number in the sample who have a bachelor's degree.What is the probability that B will equal 40?A. (50 40) (0.31)^40(0.69)^10B. (50 40) (0.69)^40 (0.31)^10C. (50 10) (0.31)^40 (0.69)^10D. (50 40) (0.69)^40 (0.31)^10E. 40(0.31)^505. A blind taste test will be conducted with 9 volunteers to determine whether people can taste a differencebetween bottled water and tap water. Each participant will taste the water from two different glassesand then identify which glass he or she thinks contains the tap water. Assuming that people cannottaste a difference between bottled water and tap water, what is the probability that at least 8 of the 9participants will correctly identify the tap water?A. 0.0020B. 0.0195C. 0.8889D. 0.9805E. 0.99806. In a certain board game, a player rolls two fair six-sided dice until the player rolls doubles (where thevalue on each die is the same). The probability of rolling doubles with one roll of two fair six-sided diceis 1/6. What is the probability that it takes three rolls until the player rolls doubles?A. (1/6)^3B. (5/6)^3C. (5/6)(5/6)(1/6)D. (5/6)^2(1/6)E. (1/6)(5/6)^2Page 107. A company that ships crystal bowls claims that bowls arrive undamaged in 95 percent of the shipments.Let the random variable G represent the number of shipments with undamaged bowls in 25 randomly se-lected shipments. Random variable G follows a binomial distribution with a mean of 23.75 shipments anda standard deviation of approximately 1.09 shipments. Which of the following is the best interpretationof the mean?A. Every shipment of 25 bowls will have 23.75 undamaged bowls.B. Every shipment of 25 bowls will have 23.75 damaged bowls.C. On average, the company receives 23.75 shipments before receiving the first shipment with adamaged bowl.D. For all possible shipments of size 25, the average number of damaged shipments is equal to23.75.E. For all possible shipments of size 25, the average number of undamaged shipments is equal to23.75.8. The transaction history at an electronic goods store indicates that 21 percent of customers purchase theextended warranty when they buy an eligible item. Suppose customers who buy eligible items are chosenat random, one at a time, until one is found who purchased the extended warranty. Let the randomvariable X represent the number of customers it takes to find one who purchased the extended warranty.Assume customers' decisions on whether to purchase the extended warranty are independent. Which ofthe following is closest to the probability that X > 3?A. 0.131B. 0.390C. 0.493D. 0.507E. 0.6249. According to a recent survey, 81 percent of adults in a certain state have graduated from high school.If 15 adults from the state are selected at random, what is the probability that 5 of them have notgraduated from high school?A. (15 5) (0.19)^15 (0.81)^5B. (15 10) (0.19)^15 (0.81)^15C. (15 5) (0.81)^5 (0.19)^10D. (15 15) (0.19)^5 (0.81)^10E. (15 5) (0.81)^5 (0.19)^1010. A recent study reported that 45 percent of adults in the United States now get all their news online. Arandom sample of 8 adults in the United States will be selected. What is the probability that 6 of theselected adults get all their news online?A. (8 6) (0.45)^8 (0.55)^2B. (8 6) (0.45)^6 (0.55)^2C. (8 2) (0.45)^2 (0.55)^8D. (8 6) (0.45)^6 (0.55)^2E. (8 8) (0.45)^8 (0.55)^6Page 115 Sampling Distributions1. For which of the following conditions is it not appropriate to assume that the sampling distribution ofthe sample mean is approximately normal?A. A random sample of 8 taken from a normally distributed populationB. A random sample of 50 taken from a normally distributed populationC. A random sample of 10 taken from a population distribution that is skewed to the rightD. A random sample of 75 taken from a population distribution that is skewed to the leftE. A random sample of 100 taken from a population that is uniform2. Researchers working for a certain airline are investigating the weight of carry-on bags. The researcherswill use the mean weight of a random sample of 800 carry-on bags to estimate the mean weight of allcarry-on bags for the airline. Which of the following best describes the effect on the bias and the varianceof the estimator if the researchers increase the sample size to 1,300?A. The bias will decrease and the variance will remain the same.B. The bias will increase and the variance will remain the same.C. The bias will remain the same and the variance will decrease.D. The bias will remain the same and the variance will increase.E. The bias will decrease and the variance will decrease.3. A bag contains chips of which 27.5 percent are blue. A random sample of 5 chips will be selected one ata time and with replacement. What are the mean and standard deviation of the sampling distributionof the sample proportion of blue chips for samples of size 5?A. The mean is 5(0.275), and the standard deviation is sqrt(5(0.275)(0.725)).B. The mean is 0.275, and the standard deviation is sqrt(5(0.275)(0.725)).C. The mean is 0.275, and the standard deviation is sqrt(0.275(0.725)/5).D. The mean is 27.5, and the standard deviation is sqrt(5(27.5)(72.5)).E. The mean is 27.5, and the standard deviation is sqrt(27.5(72.5)/5).4. In two common species of flowers, A and B, the proportions of flowers that are blue are pa and pb,respectively. Suppose that independent random samples of 50 species-A flowers and 100 species-Bflowers are selected. Let p_a_hat be the sample proportion of blue species-A flowers and p_b_hat be the sampleproportion of blue species-B flowers. What is the mean of the sampling distribution of p_a_hat - p_b_hat?A. pa - pbB. sqrt(pa/50 + pb/100)C. pa - pbD. sqrt(pa(1-pa)/50 + pb(1-pb)/100)E. sqrt(pa(1-pa)/50 + pb(1-pb)/100)5. Suppose the variance in trunk diameter of the giant sequoia tree species is 15.7 m^2, while the variancein trunk diameter of the California redwood tree species is 10.6 m^2. Let x_1_bar represent the average trunkdiameter of four randomly sampled giant sequoia trees, and let x_2_bar represent the average trunk diameterof three randomly sampled California redwood trees. If the random sampling is done with replacement,what is the standard deviation (x_1_bar - x_2_bar) of the sampling distribution of the difference in sample meansX_1_bar - X_2_bar?A. sqrt(15.7/4 - 10.6/3)Page 12B. sqrt(15.7 - 10.6)C. sqrt(15.7/4 + 10.6/3)D. sqrt(15.7 + 10.6)E. 15.7/4 + 10.6/36. A manufacturer of cell phone batteries claims that the average number of recharge cycles for its batteriesis 400. A consumer group will obtain a random sample of 100 of the manufacturer's batteries and willcalculate the mean number of recharge cycles. Which of the following statements is justified by thecentral limit theorem?A. The distribution of the number of recharge cycles for the sample is approximately normalbecause the population mean of 400 is greater than 30.B. The distribution of the number of recharge cycles for the sample is approximately normalbecause the sample size of 100 is greater than 30.C. The distribution of the number of recharge cycles for the population is approximately normalbecause the sample size of 100 is greater than 30.D. The distribution of the sample means of the number of recharge cycles is approximately normalbecause the sample size of 100 is greater than 30.E. The distribution of the sample means of the number of recharge cycles is approximately normalbecause the population mean of 400 is greater than 30.7. The normal curve shown represents the sampling distribution of a sample mean for sample size n = 25,selected at random from a population with standard deviation sigma. (Refer to the image in the originalprompt where a normal curve is shown with an x-axis span.) Which of the following is the best estimateof the standard deviation of the population, sigma?A. 3B. 6C. 15D. 30E. 758. Based on records kept at a gas station, the distribution of gallons of gas purchased by customers is skewedto the right with mean 10 gallons and standard deviation 4 gallons. A random sample of 64 customerreceipts was selected, and the sample mean number of gallons was recorded. Suppose the process ofselecting a random sample of 64 receipts and recording the sample mean number of gallons was repeatedfor a total of 100 samples. Which of the following is the best description of a dotplot created from the100 sample means?A. The dotplot is skewed to the right with mean 10 gallons and standard deviation 4 gallons.B. The dotplot is skewed to the right with mean 10 gallons and standard deviation 0.5 gallon.C. The dotplot is skewed to the right with mean 10 gallons and standard deviation 0.4 gallon.D. The dotplot is approximately normal with mean 10 gallons and standard deviation 0.5 gallon.E. The dotplot is approximately normal with mean 10 gallons and standard deviation 0.4 gallon.9. The director of a marketing department wants to estimate the proportion of people who purchase acertain product online. The director originally planned to obtain a random sample of 2,500 people whopurchased the product. However, because of budget concerns, the sample size will be reduced to 1,500people. Which of the following describes the effect of reducing the number of people in the sample?A. The variance of the sample will increase.B. The variance of the population will decrease.Page 13C. The variance of the sampling distribution of the estimator will increase.D. The variance of the sampling distribution of the estimator will decrease.E. The variance of the sampling distribution of the estimator will remain the same.10. The graph shows the population distribution of random variable X with mean 85 and standard deviation18. (The graph shows a skewed distribution). Which of the following graphs is a sampling distributionof the sample mean for samples of size 40 taken from the population?A. A graph similar to the population (skewed).B. A graph slightly less skewed.C. An approximately normal distribution centered at 85 with smaller spread.D. An approximately normal distribution centered at 85 with larger spread.E. A uniform distribution.(Note: Based on CLT, for n = 40, the sampling distribution should be approximately normal).11. Two different drugs, X and Y, are currently in use to treat a certain condition. About 7 percent ofthe people using either drug experience side effects. A random sample of 75 people using drug X anda random sample of 150 people using drug Y are selected. The proportion of people in each samplewho experience side effects is recorded. Are the sample sizes large enough to assume that the samplingdistribution of the difference in sample proportions is approximately normal?A. Yes. Both sample sizes are large enough.B. No. The sample size for drug X is large enough, but the sample size for drug Y is not.C. No. The sample size for drug Y is large enough, but the sample size for drug X is not.D. No. Neither sample size is large enough.E. There is not enough information provided to determine whether the sampling distribution isapproximately normal.12. A recent survey concluded that the proportion of American teenagers who have a cell phone is 0.27.The true population proportion of American teenagers who have a cell phone is 0.29. For samples ofsize 1,000 that are selected at random from this population, what are the mean and standard deviation,respectively, for the sampling distribution of the sample proportion of American teenagers who have acell phone?A. 0.27, sqrt(1000(0.27)(0.73))B. 0.27, sqrt((0.29)(0.71)/1000)C. 0.27, sqrt((0.27)(0.73)/1000)D. 0.29, sqrt((0.29)(0.71)/1000)E. 0.29, sqrt(1000(0.29)(0.71))13. A reading specialist wanted to estimate the mean word length, in number of letters, for an elementaryschool history textbook. The specialist took repeated random samples of size 100 words and estimated themean and standard deviation of the sampling distribution to be 4.9 letters and 0.15 letter, respectively.Based on the estimates for the sampling distribution, which of the following provides the best estimatesof the population parameters?A. Mean 4.9 letters and standard deviation 0.015 letterB. Mean 4.9 letters and standard deviation 0.15 letterC. Mean 4.9 letters and standard deviation 1.5 lettersD. Mean 0.49 letter and standard deviation 0.15 letterE. Mean 49 letters and standard deviation 15 lettersPage 14