Question

Use technology or a z-score table to answer the question. Scores on a standardized military exam are normally distributed with a mean of 57 and a standard deviation of 9. Consider a group of 4000 military students. Approximately how many students will score less than 66 on the test?

Answer 1

Approximately 3365 students will score less than 66.

The z-score is calculated using the formula
z=(X-μ)/σ, where μ is the mean and σ is the standard deviation.

For this problem, we have
z=(66-57)/9 = 9/9 = 1.00

Using a z-table (http://www.z-table.com) we see that the area to the left of, or probability less than, this is 0.8413.

To find the number of students out of 4000 that will score in this range, we multiply this probability by 4000:

0.8413(4000) = 3365.2 ≈ 3365