Question

A corporation notes that scores on an intelligence test for newly hired employees are normally distributed with a mean of 110 and a standard deviation of 20.

(a) What percentage of new employees should score above 140 on the intelligence test?
(b) What percentage of new employees should score below 95 on the intelligence test?

Answer 1

To find the percentage of new employees who should score above 140 on the intelligence test, calculate the z-score and look up the corresponding percentage. For new employees who should score below 95 on the intelligence test, follow the same steps.

Step-by-step explanation:

(a) To find the percentage of new employees who should score above 140 on the intelligence test, we need to calculate the z-score for a score of 140. The formula for calculating the z-score is:

z = (X - μ) / σ

where X is the individual score, μ is the mean, and σ is the standard deviation.

Using the given values, the z-score for a score of 140 is:

z = (140 - 110) / 20 = 1.5

Next, we can look up the corresponding percentage in the standard normal distribution table or use a calculator to find that approximately 93.32% of new employees should score above 140 on the intelligence test.

(b) To find the percentage of new employees who should score below 95 on the intelligence test, we can follow the same steps. The z-score for a score of 95 is:

z = (95 - 110) / 20 = -0.75

Looking up the corresponding percentage, we find that approximately 23.85% of new employees should score below 95 on the intelligence test.