Question

A highly selective boarding school will only admit students who place at least 2.5 standard deviations above the mean on a standardized test that has a mean of 300 and a standard deviation of 24. What is the minimum score that an applicant must make on the test to be​ accepted?

Answer 1

Answer:

The minimum score that an applicant must make on the test to be​ accepted is 360.

Step-by-step explanation:

Given : A highly selective boarding school will only admit students who place at least 2.5 standard deviations above the mean on a standardized test that has a mean of 300 and a standard deviation of 24.

To find : What is the minimum score that an applicant must make on the test to be​ accepted?

Solution :

We apply the z formula,

$z=\frac{x-\mu}{\sigma}$

Where, z value= 2.5

$\mu=300$ is the mean of the population

$\sigma=24$ is the standard deviation

x is the sample mean.

Substituting the values in the formula,

$2.5=\frac{x-300}{24}$

$2.5\times24=x-300$

$60=x-300$

$x=60+300$

$x=360$

Therefore, The minimum score that an applicant must make on the test to be​ accepted is 360.