Question

1. if the scores on a test have a mean of 26 and a standard deviation of 4, what is the z - score for a score of 18? and interpret it in context! a. 2 b. 11 c. - 2 d. - 1.41 *6. each of the three data sets represented by the three dot plots has 15 values.

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 \(x = 18\), \(\mu=26\), and \(\sigma = 4\). Then \(z=\frac{18 - 26}{4}\).

Step3: Calculate the value of the z - score

First, calculate the numerator: \(18-26=-8\). Then \(\frac{-8}{4}=-2\).

Interpretation:

A z - score of \(- 2\) means that the score of \(18\) is \(2\) standard deviations below the mean of \(26\).

Answer:

C. - 2