Question

a set of data items is normally distributed with a mean of 40 and a standard deviation of 9. convert 24 to a z-score.

z_{24} =
(do not round until the final answer. then round to the nearest hundredth as needed.)

Explanation:

Step1: Recall z - score formula

The formula for the z - score of a value \(x\) in a normally distributed data set with mean \(\mu\) and standard deviation \(\sigma\) is \(z=\frac{x - \mu}{\sigma}\).
Here, \(x = 24\), \(\mu=40\), and \(\sigma = 9\).

Step2: Substitute values into the formula

Substitute \(x = 24\), \(\mu = 40\), and \(\sigma=9\) into the formula:
\(z=\frac{24 - 40}{9}\)

Step3: Calculate the numerator

First, calculate the numerator: \(24-40=- 16\)

Step4: Calculate the z - score

Then, divide the numerator by the denominator: \(z=\frac{-16}{9}\approx - 1.78\) (rounded to the nearest hundredth)

Answer:

\(-1.78\)