(Normal Distribution, 10 points) The heights of adult men in the US are normally distributed, with a mean of 69.2 inches

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Normal Distribution 10 Points The Heights Of Adult Men In The Us Are Normally Distributed With A Mean Of 69 2 Inches 1 (163.64 KiB) Viewed 32 times

(Normal Distribution, 10 points) The heights of adult men in the US are normally distributed, with a mean of 69.2 inches and a standard deviation of 2.66 inches. The heights of adult women in the US are also normally distributed, but with a mean of 64.3 inches and a standard deviation of 2.58 inches. (a) If a certain brand of subcompact car is only designed for individuals less than 6 feet and 2 inches tall, for what percentage US men is this car designed? (b) If a particular brand of bicycle is only comfortable for individuals between 5 feet and 6.5 feet tall, what is the probability that a woman in the US would be comfortable on this bicycle? (c) Yao Ming, at 7 feet 6 inches, was the tallest player ever in the NBA. How many standard deviations above the mean is he compared with the US male population, and what percentage of men are at least as tall as he? (d) Professor Sofya is 5 feet 5 inches tall, and Professor Snyder is 5 feet 10.5 inches tall. Convert the relevant information to the standard normal N(0,1) and answer the question: who is taller relative to their genders in the US population? (e) The US Army requires women to be between 4 feet 10 inches and 6 feet 8 inches tall to enlist. What is the median height of a random US women who would be eligible to enlist? (Hint: the median is the height at which 50% of the women able to enlist are below and 50% are above.)