Question

a normal distribution of data has a mean of 90 and a standard deviation of 18. what is the approximate z - score for the value 64?
-3.6
-1.4
1.4
3.6

Explanation:

Step1: Recall the z - score formula

The z - score formula is \(z=\frac{x-\mu}{\sigma}\), where \(x\) is the data point, \(\mu\) is the mean, and \(\sigma\) is the standard deviation.

Step2: Substitute the given values into the formula

Given \(\mu = 90\), \(\sigma=18\), and \(x = 64\). Then \(z=\frac{64 - 90}{18}\).
First, calculate the numerator: \(64-90=-26\).
So, \(z=\frac{-26}{18}\approx - 1.44\approx - 1.4\) (rounded to one decimal place).

Answer:

B. - 1.4