Architects often work with physical anthropologists to design work areas that co

Question

Architects often work with physical anthropologists to design work areas that comfortably fit the largest number of people. In the United States a standard door frame has an 80 inch clearance. Assuming that male Americans heights are normally distributed with a mean of 70 inches and a standard deviation of 4 inches. 1) What percentage of the population is at risk for hitting the door frame? 2) If a pneumatic door closer is placed within the door frame that lowers the clearance by 3 inches, what percentage of the male population is now at risk for not clearing the door opening?

Explanation / Answer

Mean is 70 and s is 4

z can be found as (x-mean)/s

a) P(x>80)=P(z>(80-70)/4) or P(z>2.5) or 1-P(z<2.5), from normal distribution table we get 1-0.9938 =0.0062

b) P(x>77)=P(z>(77-70)/4) or P(z>1.75) or 1-P(z<1.75), from normal distribution table we get 1-0.9599=0.0401

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