Question

The sales of a salesman average $500 with a standard deviation of $15.2. He gets a $100 commission only if the sale exceeds $520. What is the probability the next sale will exceed $520? (please round your answer to 4 decimal places)

Answer 1

Answer 2

To find the probability that the next sale will exceed $520, we need to calculate the z-score corresponding to the value of $520 using the given average and standard deviation. Then, we can use the z-score to find the probability using a standard normal distribution table or calculator.

First, calculate the z-score using the formula:

z = (x - μ) / σ

where x is the value of $520, μ is the average of $500, and σ is the standard deviation of $15.2.

z = (520 - 500) / 15.2 z = 1.3158

Next, we can find the probability using the z-score. The probability can be obtained from a standard normal distribution table or a calculator.

Using a standard normal distribution table, the probability corresponding to a z-score of 1.3158 is approximately 0.9088.

Therefore, the probability that the next sale will exceed $520 is approximately 0.9088 (rounded to 4 decimal places).