Question

a set of data items is normally distributed with a mean of 70 and a standard deviation of 2. convert 77 to

z77=
(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 value, \(\mu\) is the mean, and \(\sigma\) is the standard deviation.

Step2: Substitute the given values into the formula

Given \(x = 77\), \(\mu=70\), and \(\sigma = 2\). Then \(z=\frac{77 - 70}{2}\).

Step3: Calculate the numerator

\(77-70=7\). So the formula becomes \(z=\frac{7}{2}\).

Step4: Perform the division

\(\frac{7}{2}=3.5\).

Answer:

\(3.5\)