The weekly mean income of a group of executives is $1,000 and the standard deviation of this group is $100. The distribution is normal. What percent of the executives have an income of $925 or less?
A)About 15%
B)About 85%
C)About 50%
D)About 23%

Question

Quizplus · Accepted Answer

To find the percentage of executives with an income of $925 or less, we calculate the Z-score: $Z = \frac{X - \mu}{\sigma} = \frac{925 - 1000}{100} = -0.75$. Looking up a Z-score of -0.75 in a standard normal distribution table or using a calculator gives us a value of about 0.2266, which translates to about 22.66% of the executives. This is closest to 23%, making option D the correct answer.

The Weekly Mean Income of a Group of Executives Is