The mean annual salary for a sample of electrical engineers is \$86,500, with a standard deviation of \$1500. The data set has a bell-shaped distribution.


b. The salaries of three randomly selected electrical engineers are \$93,500, \$85,600, and \$82,750. Find the z-score that corresponds to each salary. Determine whether any of these salaries are unusual.

Building Basic Skills and Vocabulary

A student’s grade on the Fundamentals of Engineering exam has a z-score of −0.5. Make an observation about the student’s grade.

True or False? In Exercises 7–10, determine whether the statement is true or false. If it is false, rewrite it as a true statement.

It is impossible to have a z-score of 0.

Graphical Analysis In Exercises 41 and 42, the midpoints A, B, and C are marked on the histograms at the left. Match them with the indicated z-scores. Which z-scores, if any, would be considered unusual?

z = 0, z = 2.14, z = −1.43

Explain how to transform a given x-value of a normally distributed variable x into a z-score.

Computing and Interpreting z-Scores In Exercises 39 and 40, (a) find the z-score that corresponds to each value and (b) determine whether any of the values are unusual.

Stanford-Binet IQ Scores The test scores for the Stanford-Binet Intelligence Scale are normally distributed with a mean score of 100 and a standard deviation of 16. The test scores of four students selected at random are 98, 65, 106, and 124.

Finding Probabilities for Normal Distributions In Exercises 7–12, find the indicated probabilities. If convenient, use technology to find the probabilities.

MCAT Scores In a recent year, the MCAT total scores were normally distributed, with a mean of 500.9 and a standard deviation of 10.6. Find the probability that a randomly selected medical student who took the MCAT has a total score that is (a) less than 490. Identify any unusual events in parts (a)–(c). Explain your reasoning. (Source: Association of American Medical Colleges)

Finding Probabilities for Normal Distributions In Exercises 7–12, find the indicated probabilities. If convenient, use technology to find the probabilities.

Health Club Schedule The amounts of time per workout an athlete uses a stairclimber are normally distributed, with a mean of 20 minutes and a standard deviation of 5 minutes. Find the probability that a randomly selected athlete uses a stairclimber for (a) less than 17 minutes.