Question

The distribution of heights of adult American men is approximately Normal with mean 69 inches and standard deviation 2.5 inches. What percent of men are between 64 and 66.5 inches tall?
answer choices
A. 50%B. 2.5%C. 13.5%D. 34%

Answer 1

Answer:

option C 13.5%

Step-by-step explanation:

As the heights of adults is normally distributed with mean=69 and standard deviation=2.5 so, the percent of men that are between 64 and 66.5 inches tall can be calculated as

P(64<X<66.5)=P[ (64-69)/2.5<(X-μ)/σ<(66.5-69)/2.5]

P(64<X<66.5)=P(-2<Z<-1)

P(64<X<66.5)=P(-2<Z<0)-P(-1<Z<0)

P(64<X<66.5)=0.4772-0.3413=0.1359

Thus, the percent of men are between 64 and 66.5 inches tall is 13.59%.

If we round the resultant quantity then it will be rounded to 13.6% but considering the given options, option C is most appropriate.