Question

An audio/video equipment discount store has 36 salespeople. Daily dollar sales for individual sellers enployed by the store has a normal distribution with a mean of $2000 and a standard deviation of $300. The store's management is going to implement an incentive program awarding a daily bonus to any salesperson who achieves daily sales over $2150. To four decimal places what is the probablitiy that an individual salesperson will earn a bonus on any given day?

Answer 1

The probability that an individual sales person earn the bonus by selling more than $2150 in a day is 0.3085.

Explanation:

For a normal distribution N(2000,300), a value of 2150 corresponds to a z-score of

z= (x-μ)/σ = (2150-2000)/300 = 0.5

According to the tables, we have

P(x'>z)=P(x'>0.5)=0.30854

The probability that an individual sales person earn the bonus by selling more than $2150 in a day is 0.3085.