Question

a set of data items is normally distributed with a mean of 75 and a standard deviation of 6. convert 87 to a z - score

( z _ { 87 } = )
(type an integer or a decimal )

Explanation:

Step1: Recall the z - score formula

The formula for the z - score is \(z=\frac{x-\mu}{\sigma}\), where \(x\) is the data item, \(\mu\) is the mean, and \(\sigma\) is the standard deviation.

Step2: Substitute the given values into the formula

Here, \(x = 87\), \(\mu=75\), and \(\sigma = 6\). So \(z=\frac{87 - 75}{6}\).

Step3: Calculate the numerator

\(87-75=12\). Then the formula becomes \(z=\frac{12}{6}\).

Step4: Perform the division

\(\frac{12}{6}=2\).

Answer:

\(2\)