Question

a set of data items is normally distributed with a mean of 40 and a standard deviation of 3. convert 46 to a z - score.

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

Given \(x = 46\), \(\mu=40\), and \(\sigma = 3\). Then \(z=\frac{46 - 40}{3}\).

Step3: Calculate the numerator

\(46-40=6\). So the formula becomes \(z=\frac{6}{3}\).

Step4: Calculate the z - score

\(\frac{6}{3}=2\).

Answer:

\(2\)