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?

Question

Mathematics

Mattie

5 February, 19:54

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?

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Rowan Walton · Answer 1

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

Step-by-step 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.