Question

The annual salaries earned by executes at Fortune 500 companies are normally distributed. The mean salary is $770,000 and the standard deviation is $32,000. What percent of executives earn between $770,000 and $810,000?

0.4202
0.3257
0.3944
0.3630
​

Answer 1

To find the percentage of executives who earn between $770,000 and $810,000, we need to calculate the z-scores for both salaries and use the z-score table to find the corresponding percentiles.

Step-by-step explanation:

To find the percentage of executives who earn between $770,000 and $810,000, we need to calculate the z-scores for both salaries and use the z-score table to find the corresponding percentiles.

First, we calculate the z-score for $770,000:

z = (x - μ) / σ = (770000 - 770000) / 32000 = 0

Next, we calculate the z-score for $810,000:

z = (x - μ) / σ = (810000 - 770000) / 32000 ≈ 1.25

Using the z-score table, we can find that the percentage of executives earning between $770,000 and $810,000 is approximately 0.3944, which is equivalent to 39.44%.