Humble Independent School District
AP StatisticsChapter 2 Review1. Suppose the average score on a national exam is 500 with a standard deviation of 100. If each score is increased by 20 and the result is increased by 10 percent, what are the new mean and standard deviation?(a) ? = 570, σ = 100(b) ? = 570, σ = 110(c) ? = 572, σ = 100(d) ? = 572, σ = 110(e) ? = 572, σ = 13230765759525002. The figure shows a cumulative relative frequency graph of the number of ounces of alcohol consumed per week in a sample of 150 adults who report drinking alcohol occasionally. About what percent of these adults consume between 4 and 8 ounces a week?(a) 20%(b) 40%(c) 50%(d) 60%(e) 80%3. Suppose the scores on an exam have a mean of 75 with a standard deviation of 8. If one student has a test result with a z-score of -1.5, and a second student has a test result with a z-score of 2.0, how many points higher was the second student’s result than that of the first?(a) 3.5(b) 4(c) 12 (d) 16(e) 284. Assuming that heights of professional male tennis players follow a bell-shaped distribution, arrange in ascending order:I. A height with a z-score of 1II. A height with a percentile rank of 80 percentIII. A height at the third quartile Q3(a) I, II, III(b) I, III, II(c) II, I, III(d) III, I, II(e) III, II, I5. If the heights of a population of men follow a Normal distribution and 99.7% have heights between 5'0" and 7'0", what is your estimate of the standard deviation of the heights in this population?(a) 1"(b) 3"(c) 4"(d) 6"(e) 12"6. Many professional schools require applicants to take a standardized test. Suppose that 1000 students take such a test. Several weeks after the test, Pete receives his score report: he got a 63, which placed him at the 73rd percentile. This means that(a) Pete’s score was below the median.(b) Pete did worse than about 63% of the test takers.(c) Pete did worse than about 73% of the test takers.(d) Pete did better than about 63% of the test takers.(e) Pete did better than about 73% of the test takers.42957759525007. A Normal probability plot of a set of data is shown in the figure to the right. If the distribution of points was displayed in a histogram, what would be the best description of the histogram’s shape?(a) Approximately Normal(b) Symmetric but not approximately Normal(c) Skewed Left(d) Skewed Right(e) Cannot be determined33718506477000Questions 8 – 10 refer to the following setting. The weights of laboratory cockroaches follow a Normal distribution with mean 80 grams and standard deviation 2 grams. The following figure is the Normal curve for this distribution of weights.8. Point C on this Normal curve corresponds to (a) 78 grams(b) 74 grams(c) 74 grams(d) 82 grams(e) 76 grams9. About what percent of cockroaches have weights between 76 and 84 grams?(a) 99.7%(b) 68%(c) 95%(d) 34%(e) 47.5%10. About what proportion of the cockroaches will have weights greater than 83 grams?(a) 0.0228(b) 0.0668(c) 0.1587(d) 0.9332(e) 0.0772Answers: 1. D, 2. B, 3. E, 4. E, 5. C, 6. E, 7. D, 8. A, 9. C, 10. B11. Which of the following MUST be true for a graph to be considered a density curve? (Circle all that apply)It must be symmetricIt must be skewed right or leftThe area under the curve must be 1The density curve is normalIt must be above the horizontal axis12. Which of the following MUST be true for a graph to be considered a normal distribution? (Circle all that apply)a. It must be symmetricb. It must be skewed right or leftc. The area under the curve must be 1d. Described by mean and standard deviatione. It must be above the horizontal axis 37433251289050013. Mrs. Causey asked her students how much time they had spent using a computer during the previous week. The following figure shows a cumulative relative frequency graph of her students’ responses. (a) At what percentile does a student who used her computer for 7 hours last week fall?(b) About how many hours per week of computer use represents the 80th percentile?(c) Estimate the median of the distribution.(d) Estimate the interquartile range (IQR) from the graph. Show your work.14. Rainwater was collected in water collectors at 30 different sites near an industrial complex, and the amount of acidity (pH level) was measured. The mean and standard deviation of the values are 4.60 and 1.10, respectively. When the pH meter was recalibrated back at the laboratory, it was found to be in error. The error can be corrected by adding 0.1 pH units to all of the values and then multiplying the result by 1.2. Calculate the correct pH measures.15. The standard normal distribution always has a mean of _________ and a standard deviation of _________.16. The formula to determine a z-score is: The z-score represents:-2571756432550017. The distribution of weights of 9-ounce bags of a particular brand of potato chips is approximately Normal with mean ? = 9.12 ounces and standard deviation σ = 0.05 ounce. Draw an accurate sketch of the distribution of potato chip bag weights. Be sure to label the mean, as well as the points 1, 2, and 3 standard deviations away from the mean on the horizontal axis.(a) Between what weights do the middle 68% of bags fall?(b) What percent of bags weigh less than 9.02 ounces?(c) What percent of 9-ounce bags of this brand of potato chips weigh between 8.97 and 9.17 ounces?(d) A bag that weighs 9.07 ounces is at what percentile in this distribution?18. Scores on the Wechsler Adult Intelligence Scale (a standard IQ test) are approximately normally distributed within age groups. For the 20–34 age group, the mean is 110 and the standard deviation is 25. For the 60–64 age groups, the mean is 90 and the standard deviation is 25. Sarah is 29 and her mother is 62. Sarah scores 135 on the Wechsler test, while Ann scores 120. Who has the better score, relative to her age group?19. The army reports that the distribution of head circumference among soldiers is approximately normal with mean 22.8 inches and standard deviation 1.1 inches. (a) A male soldier whose head circumference is 23.9 inches would be at what percentile? Show your method clearly. Draw a sketch to represent this percentile.(b) The army’s helmet supplier regularly stocks helmets that fit male soldiers with head circumferences between 20 and 26 inches. Anyone with a head circumference outside that interval requires a customized helmet order. What percent of male soldiers require custom helmets? Draw a sketch to represent this percent.1310640688721000(c) Find the interquartile range for the distribution of head circumference among male soldiers.20. A particular set of data has an approximately Normal distribution with a mean 20 and standard deviation of 2. Use Table A to find the proportion of observations that correspond with each question. (Find x on letter (d).) (a) x < 15(b) x > 21(c) 16 < x < 23(d) Top 10% ................
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