2) Many firms use on-the-job training to teach their employees computer programming. Suppose you work in the personnel department of a firm that just finished training a group of its employees to program, and you have been requested to review the performance of one of the trainees on the final test that was given to all trainees. The mean and standard deviation of the test scores are 81 and 3, respectively, and the distribution of scores is bell-shaped and symmetric. Suppose the trainee in question received a score of 77. Compute the trainee's z-score.

Question

A) z = -0.91
B) z = 1.33
C) z = 0.91
D) z = -1.33
Show work

Answer 1

To compute the trainee's z-score, you can use the formula for the z-score:

\[ z = \frac{(X - \mu)}{\sigma} \]

where:

• \( X \) is the score of the trainee,
• \( \mu \) is the mean of the test scores,
• \( \sigma \) is the standard deviation of the test scores.

From the information provided:

• \( X = 77 \)
• \( \mu = 81 \)
• \( \sigma = 3 \)

Now, substitute the values into the formula:

\[ z = \frac{(77 - 81)}{3} \]

Calculate \( 77 - 81 \):

\[ 77 - 81 = -4 \]

Now substitute \(-4\) into the formula:

\[ z = \frac{-4}{3} \]

Calculating that gives:

\[ z \approx -1.33 \]

Therefore, the trainee's z-score is:

\[ \boxed{D) , z = -1.33} \]