Question

a set of data items is normally distributed with a mean of 60 and a standard deviation of 10. convert 95 to a z - score.

( z_{95}=square )
(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 value, \(\mu\) is the mean, and \(\sigma\) is the standard deviation.

Step2: Substitute the given values into the formula

Given \(x = 95\), \(\mu=60\), and \(\sigma = 10\). Then \(z=\frac{95 - 60}{10}\).

Step3: Calculate the numerator

\(95-60=35\). So the formula becomes \(z=\frac{35}{10}\).

Step4: Perform the division

\(\frac{35}{10}=3.5\).

Answer:

\(3.5\)