Question

the scores on a mathematics exam have a mean of 68 and a standard deviation of 5. find the x - value that corresponds to the z - score 4.506. 113.1 22.9 90.5 63.5

Explanation:

Step1: Recall the z - score formula

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

Step2: Rearrange the formula to solve for \(x\)

From \(z = \frac{x-\mu}{\sigma}\), we can get \(x=\mu + z\sigma\).

Step3: Substitute the given values

Given \(\mu = 68\), \(z = 4.506\), and \(\sigma=5\). Then \(x=68+(4.506\times5)\).

Step4: Calculate the value of \(x\)

First, calculate \(4.506\times5 = 22.53\). Then \(x=68 + 22.53=90.53\approx90.5\).

Answer:

C. 90.5