Question: Kerbeck Automotive Sales pays its sales staff a salary plus a commission on sales. The mean biweekly commission is $990, the median $950, and the standard deviation $70. The shape of the distribution is unknown. Estimate the percent of salespeople that earn more than $885, but less than $1095 in commissions.

See Answer: The shape of the distribution is unknown, and since this is an individual outcome, we cannot use the Central Limit Theorem. Hence, the only way to approximate the probability is assuming that the distribution is at least approximately normal. We need to estimate the following probability: