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Why Not Normal?

APSTAT-YZ1PVS

At a local company, the median salary for all employees is $\$58,020$ and the standard deviation is $\$19,694$. An individual making $\$140,396$ while working at this company would be in the $95$th percentile while an individual in the $25$th percentile would be making about $\$44,735$.

Which of the following reasons might cause us to suspect that the distribution of salaries at this company is NOT approximately normal?

A

The difference between the $95$th percentile and the mean is greater than the difference between the mean and the $25$th percentile.

B

It is impossible for an individual working for this company to be earning $3$ standard deviations below the mean.

C

If the salaries were normally distributed, someone at the $95$th percentile should be making more than $\$140,396$.

D

If the salaries were normally distributed, someone at the $25$th percentile should be making less than $\$44,735$.

E

All of the above are valid reasons why we may suspect the distribution is not approximately normal.