Here's the scenario:

"A salesperson sells an average of

**1120**products a week, with a standard deviation of

**146**. He will get a bonus if, over a four-week period, the average number he sells per week is more than

**1200**. What is the probability that he will get a bonus next month?"

So I assumed I needed to find

*(*

*P**> 1200)*

*X*For the Z-score: (x -

*÷*

*μ)**= (1200 - 1120) ÷ 146 = 80 ÷ 146 = 0.55*

*σ*From the z-table: z = 0.7088

So, P(X > 1200) = 1 – P(X ≤ 1200) = 1 – P(Z ≤ 0.55) = 1 – 0.7088 = 0.2912

Thus, a probability of 29%

However, does this equation work since the 1200 is an average and not a single data point? Does the 4 (for weeks) need to be considered here? This is what's really throwing me off, and Google has not been kind.

Thank you.