Parts 2 and 3 - Height Requirements (Empirical Rule, z-scores, Applications of the Normal Curve) Part 2: 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 (b) 64.70 inches and a standard deviation of (c) 2.61 inches. B. 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 (d) _59.48 and 69.92 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 (e) 64.70 inches? 2 ptA roller coaster in the Kiddie World amusement park is designed to fit children of a specific size range. 12. The heights of 5year old boys in the United States are approximatelyr normally distributed with a mean of If) _41.90 inches and a standard deviation of [g] _2.19 inches. Label the normal curve below to show the oomplete distribution of heights out to four standard deviations in each direction of the mean. [3 pt} m The roller coaster ts children from 38 inches to 5D inches tall, so children shorter than SS inches or taller than 5D inches won't be allowed to ride it. place. 13 a What is the z-soore of a 5year old boy.r who is BS inches tall? Show 1grour calculations. Round to one decimal {4 at} round. Refer to the ztable that was included with the Stats 3 handout. {22:} What percentage of 5year old boys have heights below 38 inches? {too short to ride the coaster]. Do not What is the 2-score of a 5year old boy who is 5D inches tall? Round to one decimal plaoe. RI} Refer to the ztable that was included with the Stats 3 handout. {4 14-h What percentage of 5year old boys have heights above 5D inches? {too tall to ride the master}. Do not round. RI} What percentage of 5year old boys will be allowed to ride the roller coaster? Do not round 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)