Quiz Content
Question 1
A statistics teacher selects a sample of 132 students. He determines that the population mean is 98 with a standard deviation of
48 . Based on the information given, what will be the -score if the statistics teacher decides to compute a z-transformation?
(A) 4.18
(B) 8.13
© 11.48
(D) 1.39

Question

Quiz Content
Question 1
A statistics teacher selects a sample of 132 students. He determines that the population mean is 98 with a standard deviation of
48 . Based on the information given, what will be the

-score if the statistics teacher decides to compute a z-transformation?
(A) 4.18
(B) 8.13
© 11.48
(D) 1.39

UpStudy AI · Accepted Answer

Let the hypothesis be that a student’s score (or the sample mean) is $$ 132 $$ and the population parameters are given as a mean $$\mu=98$$ and a standard deviation $$\sigma=48$$. When a z-transformation is computed for a sample mean, the formula is

$$
z=\frac{\bar{x}-\mu}{\sigma/\sqrt{n}}.
$$

In this problem the value being transformed is $$ \bar{x}=132 $$, the population mean is $$\mu=98$$, the population standard deviation is $$\sigma=48$$, and the sample size is $$ n=132 $$.

Step 1. Compute the standard error:

$$
SE=\frac{\sigma}{\sqrt{n}}=\frac{48}{\sqrt{132}}.
$$

We can approximate $$\sqrt{132}$$. Since

$$
\sqrt{132}\approx 11.489,
$$

we have

$$
SE\approx \frac{48}{11.489}\approx 4.175.
$$

Step 2. Compute the difference between the sample mean and the population mean:

$$
\bar{x}-\mu=132-98=34.
$$

Step 3. Calculate the z-score:

$$
z=\frac{34}{4.175}\approx8.14.
$$

This value is closest to 8.13, which corresponds to option (B).
The z-score is approximately 8.13.

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