Question

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% of the incomes lie between what two incomes

Answer 1

Answer:

68% of the incomes lie between $36,400 and $38,000.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ =  $37,200

Standard Deviation, σ = $800

We are given that the distribution of SAT score is a bell shaped distribution that is a normal distribution.

Empirical rule:

• Almost all the data lies within three standard deviation of mean for a normally distributed data.
• About 68% of data lies within one standard deviation of mean.
• About 95% of data lies within two standard deviation of mean.
• About 99.7% of data lies within three standard deviation of mean.

Thus, 68% of data lies within one standard deviation.

$\mu \pm \sigma\\=37200 \pm 800\\=(36400,38000)$

Thus, 68% of the incomes lie between $36,400 and $38,000.