Question

In a survey men in a certain country (ages 20-29), the mean height was 62.8 inches with a standard deviation of 2.8 inches, what height represents the 99th percentile?

Answer 1

the height that represents the 99th percentile is 69.324 inches

Explanation:

Given that :

the mean height = 62.8 inches

standard deviation = 2.8 inches

For 99th percentile;

Let X be the random variable;

SO, P(Z≤ z) = 0.99

From the standard normal z tables

P(Z )= 2.33

The standard z score formula is :

`z = (X- \mu)/(\sigma)`

`2.33 = (X- 62.8)/(2.8)`

2.33 × 2.8 = X - 62.8

6.524 = X - 62.8

6.524 +62.8 = X

69.324 = X

X = 69.324

Therefore; the height that represents the 99th percentile is 69.324 inches