Question

a set of data items is normally distributed with a mean of 70 and a standard deviation of 4. convert 71 to a z-score.
z_{71} = \square
(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 normal distribution is \(z=\frac{x - \mu}{\sigma}\), where \(\mu\) is the mean and \(\sigma\) is the standard deviation.

Step2: Identify values

We are given that \(x = 71\), \(\mu=70\), and \(\sigma = 4\).

Step3: Substitute values into formula

Substitute \(x = 71\), \(\mu = 70\), and \(\sigma=4\) into the z - score formula: \(z=\frac{71 - 70}{4}\)

Step4: Simplify the expression

First, calculate the numerator: \(71-70 = 1\). Then, divide by the denominator: \(\frac{1}{4}=0.25\)

Answer:

\(0.25\)