Chapter 8.5, Problem 30E

(a)

To determine

To find the percentage of population scores between 400 and 500 marks in aptitude test.

Answer to Problem 30E

The percentage of population scores between 400 and 500 marks in aptitude test is 34.45 %

Explanation of Solution

Given information: Mean $\mu =498$ and standard deviation $\sigma =100$ of the normal distribution.

Formula Used: The probability density function for a normal distribution with mean $\mu$

and standard deviation $\sigma$ is: $f(x)=\frac{1}{\sigma \sqrt{2\pi }}{e}^{\frac{-{(x-\mu )}^2}{2{\sigma }^2}}=\frac{1}{\sigma \sqrt{2\pi }}{e}^{\frac{-z^2}{2}};z=\frac{x-\mu }{\sigma }$

Calculation :

Here, $\mu =498$ and $\sigma =100$

When $x=400$ , $z=\frac{400-498}{100}=-0.98$

When $x=500$ , $z=\frac{500-498}{100}=0.02$

Between $z=-0.98\text{to}z=0.02$ , the area under the normal curve is 34.45 %

Hence, the percentage of population scores between 400 and 500 marks in aptitude test is 34.45 %