Question

The average height of young adult males has a normal distribution with a standard deviation of 2.5 inches. You want to estimate the mean height of students at your college or university to within one inch with 93 per cent confidence. How many male students must you measure?

Short answer

$21$male adult students should be measured.

Step-by-step solution

Introduction 

The standard deviation is a proportion of how much variety or scattering of a bunch of values. A low standard deviation shows that the values will generally be close to the mean of the set, while an elevated expectation deviation demonstrates that the values are fanned out over a more extensive territory.

Explanation 

Within the population,

The average height of young adult males has a normal distribution with a standard deviation of$2.5$inches.

To estimate the mean height of students within one inch with confidence level =$93\%$

Let the number of students to be measured be n,

By using,

$n=\frac{z^2{\sigma }^2}{EB{M}^2}$

on substituting the values,

$n=\frac{{1.812}^2\times {2.5}^2}{1^2}=21$

$21$male adult students should be measured.