Question

a set of data items is normally distributed with a mean of 70 and a standard deviation of 6. convert 82 to a z - score.

z_{82}=\square
(type an integer or a decimal.)

Explanation:

Step1: Recall the z - score formula

The z - score formula 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 \(x = 82\), \(\mu=70\), and \(\sigma = 6\). Then \(z=\frac{82 - 70}{6}\).

Step3: Calculate the numerator

\(82-70=12\). So the formula becomes \(z=\frac{12}{6}\).

Step4: Perform the division

\(\frac{12}{6}=2\).

Answer:

\(2\)