Question

3)

The height of an adult male in the United States is approximately normally distributed with a mean of 69.3 inches and a standard deviation of 2.8 inches.

Find the percentile P₉₀ for the heights of adult males in the United States.

Provided your answer in inches, rounded to 2 decimal places.

Answer 1

Given,

= 69.3 , = 2.8

We convert this to standard normal as

P(X < x) = P(Z < ( x - ) / )

P90 = P(X < x) = 0.90

P(Z< ( x - ) / ) = 0.90

From Z table, z-score for the probability of 0.90 is 1.2816

( x - ) / = 1.2816

(X - 69.3) / 2.8 = 1.2816

Solve for X

X = 72.89