The distribution of the annual incomes of a group of middle management employees approximated a normal distribution with a mean of $37,200 and a standard deviation of $800. About 68 percent of the incomes lie between what two incomes?
A) $30,000 and $40,000
B) $36,400 and $38,000
C) $34,800 and $39,600
D) $35,600 and $38,800

Question

Quizplus · Accepted Answer

Since it's a normal distribution, we can use the empirical rule which states that approximately 68% of the data falls within 1 standard deviation of the mean. Thus, the incomes between $37,200- $800 = $36,400 and $37,200 + $800 = $38,000 will contain about 68% of the incomes. Therefore, the correct option is B, $36,400 and $38,000.

The Distribution of the Annual Incomes of a Group of Middle