Question

a set of data items has a mean of 65 and a standard deviation of 6 convert the data item 44 to a z - score

( z _ { 44 } = 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 item, \(\mu\) is the mean, and \(\sigma\) is the standard deviation.

Step2: Substitute the given values into the formula

Here, \(x = 44\), \(\mu=65\), and \(\sigma = 6\). So, \(z=\frac{44 - 65}{6}\).

Step3: Calculate the numerator

\(44-65=-21\). Then the formula becomes \(z=\frac{-21}{6}\).

Step4: Perform the division

\(\frac{-21}{6}=-3.5\)

Answer:

\(-3.5\)