Question

A set of data items is normally distributed with a mean of 500. Find the data item in this distribution that corresponds to the given z-score. z = 2, if the standard deviation is 40.

Answer 1

Answer:

580.

Step-by-step explanation:

The provided information are:

Population mean $(\mu)$ = 500

Population standard deviation $(\sigma)$ = 40

z-score = 2

The formula to calculate the z-score is:

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

x = data item.

The data item can be computed as:

$2=\frac{x-500}{40} \\\\80=x-500\\x=580$

Hence, the data item is 580.