A survey found that women's heights are normally distributed with mean 63.9 in. and standard deviation 3.6 in. The survey also found that men's heights are normally distributed with mean 69.7 in. and standard deviation 3.6 in. Consider an executive jet that seats six with a doorway height of 55.9 in. Complete parts (a) through (c) below. a. What percentage of adult men can fit through the door without bending? The percentage of men who can fit without bending is 0.02%. (Round to two decimal places as needed.) b. Does the door design with a height of 55.9 in. appear to be adequate? Why didn't the engineers design a larger door?
Accepted Solution
A:
Answer:a: 0.1%b. No it does notc. Probably for safety reasonsStep-by-step explanation:for women: z = (55.9 - 63.9)/3.6 = -2.22The p-value for z = -2.22 is 0.0132, so only 1.32% of women could walk through without bendingfor men: z = (55.9 - 69.7)/3.6 = -3.83The p-value for z = -3.83 is 0.001, so only 0.1% of men could walk through without bending