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Name _______________________________ AP Statistics – C hapter 2 Review Date _____________________ 1. The heights of American men aged 18 to 24 are approximately Normally distributed with a mean of 68 inches and a standard deviation of 2.5 inches. Only about 5% of young men have heights outside the range (a) 65.5 inches to 70.5 inches (b) 63 inches to 73 inches (c) 60.5 inches to 75.5 inches (d) 58 inches to 78 inches (e) none of the above 2. U se the information in the previous problem. About what percentage of the men are over 70.5 inches tall? (a) 2.5 (b) 5 (c) 16 (d) 32 (e) 68 3. The graph at right is a Normal probability plot for the amount of rainfall (in acre-feet) obtained from 26 randomly selected clouds that were seeded with silver oxide. Which of the following statements about the shape of the rainfall distribution is true? (a) The distribution is Normal. (b) The distribution is approximately Normal. (c) The distribution is skewed left. (d) The distribution has no potential outliers. (e) The distribution is skewed right. 4. The cumulative relative frequency graph at right shows the distribution of lengths (in centimeters) of fingerlings at a fish hatchery. The interquartile range for this distribution is approximately: (a) 0.18 to 0.85 centimeters (b) 5 to 7 centimeters (c) 5.5 to 6.7 centimeters (d) 1.2 centimeters (e) 2 centimeters 5. According to data, the mean song length is 4.23 minutes, and the standard deviation is 1.38 minutes. A music lover who wants to create a mix of songs wants to have 5 seconds of silence between songs, so he needs to add five seconds to the length of each song. He also wants to express the times in seconds, rather than minutes. Find the mean and standard deviation of the transformed data. 6. A study of elite distance runners found a mean body weight of 63.1 kilograms (kg), with a standard deviation of 4.8 kg. (a) Assuming that the distribution of weights is approximately Normal, make an accurate sketch of the weight distribution with the horizontal axis marked in kilograms. (b) Use the 68–95–99.7 rule to find the proportion of runners whose body weight is between 48.7 and 67.9 kg. (c) What proportion of runners have body weights below 60 kg? (d) What proportion of runners have body weights above 70 kg? (e) C alculate and i nterpret the 45th percentile of the runners’ body weight distribution. 7. A Normal probability plot for the amount of lactic acid in a sample of 30 pieces of cheese is shown below. Is the lactic acid distribution approximately Normal? Justify your answer. 8. Below are cumulative frequency graphs for the age distributions of the populations of France and the Philippines. (a) Find and interpret the age that represents the 40th percentile for both the Philippines and France. (b) Would it be more unusual for a person to be 20 years old in the Philippines or France? Justify your answer. 9. The scores of a reference population on the Wechsler Intelligence Scale for C hildren (WISC ) are approximately Normally distributed with μ = 100 and σ = 15. (a) What score would represent the 50th percentile? Explain. (b) A score in what range would represent the top 1% of the scores? (c) What proportion of the reference population has WISC scores below 110? (d) What proportion of the reference population has WISC scores between 80 and 110?
