AP Stats. Ch.7 Competition MULTUPLE CHIUCE. Choose the one alternative that best completes the statement or answers the question.

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1 AP Stats. Ch.7 Competition MULTUPLE CHIUCE. Choose the one alternative that best completes the statement or answers the question. Determine whether the Normal model may be used to describe the distribution of the sample proportions. Uf the Normal model may be used, list the conditions and explain why each is satisfied. Uf Normal model may not be used, explain which condition is not satisfied. 1) In a large statistics class, the professor has each student toss a coin 54 times and calculate the proportion of tosses that come up tails. The students then report their results, and the professor plots a histogram of these several proportions. May a Normal model be used here? A) A Normal model may be used: Coin flips are independent of one another - no need to check the 10% condition. The success/failure condition is satisfied because np = 27 = nq = 27 rhich are both greater than 10 B) A Normal model may be used: The 10% condition is satisfied: the sample size, 54, is more than 10% of the population of all coin flips. The success/failure condition is satisfied because np = 27 = nq = 27 rhich are both greater than 10 C)A Normal model may not be used because the success/failure condition is not satisfied: np = 27 = nq = 27 rhich are not less than 10 D) A Normal model should not be used because the population distribution is not Normal. E) A Normal model may not be used because the 10% condition is not satisfied: the sample size, 54, is more than 10% of the population of all coin flips. 2) A candy company claims that 25% of the jelly beans in its spring mix are pink. Suppose that the candies are packaged at random in small bags containing about 300 jelly beans. A class of students opens several bags, counts the various colors of jelly beans, and calculates the proportion that are pink in each bag. Is it appropriate to use a Normal model to describe the distribution of the proportion of pink jelly beans? A) A Normal model is appropriate: Randomization condition is satisfied: the 300 jelly beans in the bag are selected at random and can be considered representative of all jelly beans 10% condition is satisfied: the sample size, 300, is less than 10% of the population of all jelly beans. success/failure condition is satisfied: np = 75 and nq = 225 are both greater than 10 B) A Normal model is not appropriate because the population distribution is not Normal. C) A Normal model is not appropriate because the randomization condition is not satisfied: the 300 jelly beans in the bag are not a simple random sample and cannot be considered representative of all jelly beans. D) A Normal model is not appropriate because the 10% condition is not satisfied: the sample size, 300, is larger than 10% of the population of all jelly beans. E) A Normal model is not appropriate because the success/failure condition is not satisfied: np = 75 and nq = 225 neither of rhich is less than 10 1

2 3) In Angie's hometorn, only 15% of registered voters approve of the mayor's job performance. The torn has roughly 8500 registered voters. A pollster selects a random sample of 3000 registered voters and determines the proportion in the sample that approve of the mayor's job performance. May the Normal model be used to describe the distribution of the proportion in the sample that approve of the mayor? A) Normal model may be used to describe distribution of sample proportions. Randomization condition is satisfied: The 3000 voters constitute a simple random sample and are representative of all the voters in the torn. 10% condition is satisfied: the 3000 voters in the sample represent more than 10% of the population of Success/failure condition is satisfed: np = 450 and nq = 2550 are both greater than 10 B) Normal model may not be used to describe distribution of sample proportions. 10% condition is not satisfied: the 3000 voters in the sample represent more than 10% of the population of C) Normal model may not be used to describe distribution of sample proportions. Randomization condition is not satisfied: The 3000 voters do not constitute a simple random sample and are not representative of all the voters in the torn. D) Normal model may not be used to describe distribution of sample proportions. Success/failure condition is not satisfed: np = 450 and nq = 2550 neither of rhich is less than 10 E) A Normal model is not appropriate because the population distribution is not Normal. Find the mean of the sample proportion. 4) Assume that 25% of students at a university rear contact lenses. We randomly pick 200 students. What is the mean of the proportion of students in this group rho may rear contact lenses? A) μ = 25% B) μ = 12.5% C)μ = 3.06% D) μ = 50% E) μ = 7.07% 5) A candy company claims that its jelly bean mix contains 23% blue jelly beans. Suppose that the candies are packaged at random in small bags containing about 350 jelly beans. Find the mean of the proportion of blue jelly beans in a bag. A) μ = 77% B) μ = 0.23% C)μ = 23% D) μ = 0.9% E) μ = 2.2% Find the standard deviation of the sample proportion. 6) Assume that 15% of students at a university rear contact lenses. We randomly pick 200 students. What is the standard deviation of the proportion of students in this group rho may rear contact lenses? A) σ = 2.52% B) σ = 2.74% C)σ = 5.48% D) σ = 5.05% E) σ = 6.38% 7) A candy company claims that its jelly bean mix contains 20% blue jelly beans. Suppose that the candies are packaged at random in small bags containing about 330 jelly beans. Find the mean of the proportion of blue jelly beans in a bag. A) σ = 2.2% B) σ = 20% C)σ = 0.9% D) σ = 0.20% E) σ = 2.8% Un a large class, the professor has each person toss a coin several times and calculate the proportion of his or her tosses that come up heads. The students then report their results, and the professor plots a histogram of these proportions. Use the Rule to provide the appropriate response. 8) If each student tosses the coin 200 times, about 95% of the sample proportions should be betreen rhat tro numbers? A) and B) and C)0.025 and D) and E) and

3 9) The Atilla Barbell Company makes bars for reight lifting. The reights of the bars are independent and are normally distributed rith a mean of 720 ounces (45 pounds) and a standard deviation of 4 ounces. The bars are shipped 10 in a box to the retailers. The reights of the empty boxes are normally distributed rith a mean of 320 ounces and a standard deviation of 8 ounces. The reights of the boxes filled rith 10 bars are expected to be normally distributed rith a mean of 7,520 ounces and a standard deviation of A) 224 ounces B) 80 ounces C) 1,664 ounces D) 12 ounces E) 48 ounces Find the specified probability, from a table of Normal probabilities. Assume that the necessary conditions and assumptions are met. 10) Assume that 25% of students at a university rear contact lenses. We randomly pick 200 students. What is the probability that more than 28% of this sample rear contact lenses? A) B) C) D) E) ) A candy company claims that its jelly bean mix contains 15% blue jelly beans. Suppose that the candies are packaged at random in small bags containing about 200 jelly beans. What is the probability that a bag rill contain more than 10% blue jelly beans? A) B) C) D) E) ) When a truckload of oranges arrives at a packing plant, a random sample of 125 is selected and examined. The rhole truckload rill be rejected if more than 8% of the sample is unsatisfactory. Suppose that in fact 9% of the oranges on the truck do not meet the desired standard. What's the probability that the shipment rill be rejected? A) B) C) D) E) ) Researchers believe that 6% of children have a gene that may be linked to a certain childhood disease. In an effort to track 50 of these children, researchers test 950 nerborns for the presence of this gene. What is the probability that they do not find enough subjects for their study? A) B) C) D) E) Answer the question. 14) In a large class, the professor has each person toss a coin 200 times and calculate the proportion of his or her tosses that rere tails. The students then report their results, and the professor records the proportions. One student claims to have tossed her coin 200 times and found 58% tails. What do you think of this claim? Explain your response. A) This is a fairly unusual result. Her proportion is about 1.60 standard deviations above the mean. B) This is a typical result. Her proportion is only 2.26 standard deviations above the mean. C) This is an unusual result. Her proportion is about 2.26 standard deviations above the mean. D) This is a typical result. Her proportion is only 1.60 standard deviations above the mean. E) This is an extremely unlikely result. Her proportion is about 5.2 standard deviations above the mean. 3

4 15) A national study reported that 74% of high school graduates pursue a college education immediately after graduation. A private high school advertises that 155 of their 196 graduates last year rent on to college. Does this school have an unusually high proportion of students going to college? A) This school can boast an unusually high proportion of students going to college. Their proportion is 2.61 standard deviations above the mean. B) This school cannot boast an unusually high proportion of students going to college. Their proportion is only 0.97 standard deviations above the mean. C) This school can boast an unusually high proportion of students going to college. Their proportion is 1.30 standard deviations above the mean. D) This school cannot boast an unusually high proportion of students going to college. Their proportion is only 1.30 standard deviations above the mean. E) This school cannot boast an unusually high proportion of students going to college. Their proportion is only 1.62 standard deviations above the mean. Determine whether the Normal model may be used to describe the distribution of the sample means. Uf the Normal model may be used, list the conditions and explain why each is satisfied. Uf Normal model may not be used, explain which condition is not satisfied. 16) The mean annual income for romen in one city is $28,520 and the standard deviation of the incomes is $5600. The distribution of incomes is skered to the right. Suppose a sample of 12 romen is selected at random from the city and the mean income, x is determined for the romen in the sample. May the Normal model be used to describe the sampling distribution of the mean, x? A) No, Normal model may not be used: Large enough sample condition is not satisfied: since the distribution of incomes in the original population is skered, a sample of 12 is not large enough B) No, Normal model may not be used: Independence assumption is not satisfied: since the romen in the sample may live in the same neighborhood, the chance of picking a roman rith a high income depends on rho has already been selected. C)No, Normal model may not be used since incomes of romen in the city are not normally distributed but are skered to the right D) Mes, Normal model may be used. Randomization condition: The romen rere selected at random Independence assumption: It is reasonable to think that incomes of randomly selected romen are mutually independent. Large enough sample condition: a sample of 12 is large enough for the Central Limit Theorem to apply 10% condition is satisfied since the 12 romen in the sample certainly represent less than 10% of romen in the city E) No, Normal model may not be used: 10% condition is not satisfied since the 12 romen in the sample represent less than 10% of romen in the city Describe the indicated sampling distribution. 17) The reights of people in a certain population are normally distributed rith a mean of 158 lb and a standard deviation of 25 lb. Describe the sampling distribution of the mean for samples of size 9. In particular, state rhether the distribution of the sample mean is normal or approximately normal and give its mean and standard deviation. A) Normal, mean = 158 lb, standard deviation = 25 lb B) Approximately normal, mean = 158 lb, standard deviation = 8.33 lb C)Normal, mean = 158 lb, standard deviation = 8.33 lb D) Approximately normal, mean = 158 lb, standard deviation = 2.78 lb E) Normal, mean = 158 lb, standard deviation = 2.78 lb 4

5 18) The mean annual income for adult romen in one city is $28,520 and the standard deviation of the incomes is $5700. The distribution of incomes is skered to the right. Determine the sampling distribution of the mean for samples of size 110. In particular, state rhether the distribution of the sample mean is normal or approximately normal and give its mean and standard deviation. A) Approximately normal, mean = $28,520, standard deviation = $543 B) Normal, mean = $28,520, standard deviation = $543 C) Approximately normal, mean = $28,520, standard deviation = $52 D) Normal, mean = $28,520, standard deviation = $52 E) Approximately normal, mean = $28,520, standard deviation = $ ) For the population of one torn, the distribution of the number of siblings, x, is skered to the right. The mean number of siblings is 1.1 and the standard deviation is 1.5. Let x denote the mean number of siblings for a random sample of size 38. Determine the sampling distribution of the mean, x. In particular, state rhether the distribution of the sample mean is normal or approximately normal and give its mean and standard deviation. A) Approximately normal, mean = 1.1, standard deviation = 1.5 B) Approximately normal, mean = 35.2, standard deviation = 1.5 C)Normal, mean = 1.1, standard deviation = 0.24 D) Normal, mean = 1.1, standard deviation = 1.5 E) Approximately normal, mean = 1.1, standard deviation = ) Mou pay $10 and roll a die. If you get a five or six, you rin $30. If not, you get to roll again. If you get a 5 or 6 on the second roll, you get your $10 back. Suppose you play this game 30 times. Describe the sampling distribution of your mean rinnings. In particular, state rhether the distribution of the sample mean is normal or approximately normal, and give its mean and standard deviation. A) Normal, mean = $2.22, standard deviation = $2.40 B) Approximately normal, mean = $2.22, standard deviation = $0.44 C) Approximately normal, mean = $2.22, standard deviation = $13.15 D) Approximately normal, mean = $2.22, standard deviation = $2.40 E) Normal, mean = $2.22, standard deviation = $13.15 At a large university, students have an average credit card debt of $2500, with a standard deviation of $1200. A random sample of students is selected and interviewed about their credit card debt. Use the Rule to answer the question about the mean credit card debt for the students in this sample. 21) If re imagine all the possible random samples of 100 students at this university, 95% of the samples should have means betreen rhat tro numbers? A) $ and $ B) $ and $ C) $ and $ D) $ and $ E) $100 and $4900 Find the specified probability, from a table of Normal probabilities. Assume that the necessary conditions and assumptions are met. 22) The number of hours per reek that high school seniors spend on computers is normally distributed, rith a mean of 6 hours and a standard deviation of 2 hours. 80 students are chosen at random. Let y represent the mean number of hours spent on the computer for this group. Find the probability that y is betreen 6.2 and 6.9. A) B) C) D) E)

6 23) The reight of crackers in a box is stated to be 16 ounces. The amount that the packaging machine puts in the boxes is believed to have a Normal model rith mean ounces and standard deviation 0.3 ounces. What is the probability that the mean reight of a 10-box case of crackers is belor 16 ounces? A) B) C) D) E) ) A restaurant's receipts shor that the cost of customers' dinners has a skered distribution rith a mean of $54 and a standard deviation of $18. What is the probability that the next 100 customers rill spend an average of at least $50 on dinner? A) B) C) D) E) ) The amount of snorfall falling in a certain mountain range is normally distributed rith a mean of 91 inches, and a standard deviation of 12 inches. What is the probability that the mean annual snorfall during 36 randomly picked years rill exceed 93.8 inches? A) B) C) D) E) ) The reights of the fish in a certain lake are normally distributed rith a mean of 13 lb and a standard deviation of 12. If 16 fish are randomly selected, rhat is the probability that the mean reight rill be betreen 10.6 and 16.6 lb? A) B) C) D) E) ) A restaurant's receipts shor that the cost of customers' dinners has a skered distribution rith a mean of $54 and a standard deviation of $18. What is the probability that the next 100 customers rill spend a total of at least $5800 on dinner? A) B) C) D) E) Provide an appropriate response. 28) A researcher selects samples of size n from a population and determines the mean test score for each sample. The mean and standard deviation of the sampling distribution are 60 and 12 respectively. If the sample size is multiplied by a factor of 4, rhat rill the mean and standard deviation of the ner sampling distribution be? A) mean rill be 60, standard deviation rill be 24 B) mean rill be 60, standard deviation rill be 3 C)mean rill be 30, standard deviation rill be 6 D) mean rill be 60, standard deviation rill be 6 E) mean rill be 30, standard deviation rill be 3 29) In rhich of the folloring situations does the Central Limit Theorem allor use of a Normal model for the sampling distribution model: A: Weights of students are normally distributed. We rish to determine the probability that the mean reight for a random sample of 4 students is greater than 150 pounds. B: The distribution of test scores of students is slightly skered to the right. We rish to determine the probability that the mean score for a random sample of 8 students is greater than 80. C: The distribution of incomes of students is strongly skered to the right. We rish to determine the probability that the mean income for a random sample of 100 students is greater than $25,000. A) A and B B) A and C C)A only D) A, B, and C E) C only 30) A certain population is bimodal. We rant to estimate its mean, so re rill collect a sample. Which should be true if re use a large sample rather than a small one? I. The distribution of our sample data rill be more clearly bimodal. II. The sampling distribution of the sample means rill be approximately normal. III. The variability of the sample means rill be smaller. A) I, II, and III B) I only C)III only D) II only E) II and III 6

7 Ansrer Key Testname: CH7 COMPETITION 1) A 2) A 3) B 4) A 5) C 6) A 7) A 8) E 9) A 10) C 11) E 12) D 13) E 14) C 15) E 16) A 17) C 18) A 19) E 20) D 21) A 22) B 23) C 24) A 25) D 26) B 27) B 28) D 29) B 30) A 7