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Part 2 - Height Requirements (Empirical Rule, z-scores, Applications of the Normal Curve) (Questions 8-16) Vehicle (Questions 8-11) A vehicle is designed to fit adults of a specific size range. The heights of adult women in the United States are approximately normally distributed with a mean of 65 inches and a standard deviation of 2.4 inches. 8. Label the normal curve to 3 standard deviations in each direction to reflect this distribution of heights. (3 pt) 9. According to the Empirical Rule (68-95-99.7 Rule), if a vehicle only accommodates people who are between 60.2 inches and 69.8 inches tall, what percentage of adult women in the United States will fit? (2 pt) 10. According to the Empirical Rule (68-95-99.7 Rule), what heights would the vehicle have to accommodate in order to fit the middle 68% of adult women in the United States? State the lowest and highest heights. (4 pt) 11. What percentage of adult women in the United States have a height of less than 65 inches? (2 pt) 3Roller Coaster (Questions 12-16) A roller coaster in the Kiddie World amusement park is designed to fit children of a specific size range. 12. The heights of 5-year old boys in the United States are approximately normally distributed with a mean of 43 inches and a standard deviation of 1.8 inches. Label the normal curve below to show the complete distribution of heights out to four standard deviations in each direction of the mean. (3 pt) The roller coaster fits children from 38 inches to 50 inches tall, so children shorter than 38 inches or taller than 50 inches won't be allowed to ride it. 13-a What is the z-score of a 5-year old boy who is 38 inches tall? Show your calculations. Round to one decimal place. (4 pt) 13-b |What percentage of 5-year old boys have heights below 38 inches? (too short to ride the coaster). Do not round. Refer to the z-table that was included with the Stats 3 handout. (2 pt) 14-a |What is the z-score of a 5-year old boy who is 50 inches tall? Round to one decimal place. (4 pt) 14-b | What percentage of 5-year old boys have heights above 50 inches? (too tall to ride the coaster). Do not round. Refer to the z-table that was included with the Stats 3 handout. (4 pt) 15 What percentage of 5-year old boys will be allowed to ride the roller coaster? Do not round. (4 pt) 16 Assume there are 1.9 million 5-year old boys in the United States. How many of the boys are the right height to fit on the coaster (38 in to 50 in tall)? Round your results to the nearest thousand boys. Show your calculations. Label your result. (4 pt) 4