Question

a set of data items is normally distributed with a mean of 75 and a standard deviation of 8. convert 83 to a z - score.

z83 = □
(type an integer or a decimal.)

Explanation:

Step1: Recall the z - score formula

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

Step2: Substitute the given values into the formula

Given \(x = 83\), \(\mu=75\), and \(\sigma = 8\). Then \(z=\frac{83 - 75}{8}\).

Step3: Calculate the numerator

\(83-75=8\). So the formula becomes \(z=\frac{8}{8}\).

Step4: Calculate the z - score

\(\frac{8}{8}=1\).

Answer:

\(1\)