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

Step2: Identify the values of \(x\), \(\mu\), and \(\sigma\)

Given \(x = 46\), \(\mu=40\), and \(\sigma = 3\).

Step3: Substitute the values into the formula

\(z=\frac{46 - 40}{3}\)
\(z=\frac{6}{3}\)
\(z = 2\)

Answer:

\(2\)