94. Statisticians' Salaries. If you enjoy statistics, you may want to become a statistician. The U.S. Census Bureau reported in 2014 that the median salary for mathematicians and statisticians was about $86,000. Income data is usually right-skewed, so we may safely assume that the mean is higher. Suppose the salaries of statisticians have a mean of and a standard deviation of .

Suppose we take samples of size 100 statisticians. Find the probability that the sample mean salary will have the following values: