Question

A person must score in the upper 7% of the population on an admissions test to qualify for membership in society catering to highly intelligent individuals. If test scores are normally distributed with a mean of 110 and a standard deviation of 5, what is the minimum score a person must have to qualify for the society

Answer 1

Answer: The minimum score a person must have to qualify for the society = 147.4

Explanation:

Let X be the test scores.

As per given,

X is normally distributed.

Mean
`(\mu) = 110`

`\sigma=5`

`$$\begin{array}{l}\quad P(z>2)=0.07 \\\therefore \quad 1-P(z<2)=0.07 \\\therefore \quad P(2<2)=1-0.07 \\\therefore \quad P(2<2)=0.93 \\\qquad \begin{aligned}P(z<1.48) &=0.93[\text { using } z- \text { -table] } . \\z=1.48 \\\text { let } z &=(x-\mu)/(\sigma) \\x &=\mu+2 \sigma \\x &=140+(1.48)(5) \\x &=147.4\end{aligned}\end{array}$$`

The minimum score a person must have to qualify for the society = 147.4