Question

The annual commissions per salesperson employed by a retailer of mobile communication devices averaged $40,000, with a standard deviation of $5,000. What percent of the salespersons earn between $32,000 and $42,000?

Answer 1

To find the percent of salespersons earning between $32,000 and $42,000, we calculate the Z-scores for these values and use the standard normal distribution table to find the corresponding probabilities. The percent of salespersons earning between $32,000 and $42,000 is approximately 60%.

Step-by-step explanation:

To find the percent of salespersons earning between $32,000 and $42,000, we need to find the Z-scores corresponding to these values and use the standard normal distribution table.

First, we calculate the Z-score for $32,000:

Z = (X - μ) / σ = (32,000 - 40,000) / 5,000 = -1.6

Next, we calculate the Z-score for $42,000:

Z = (X - μ) / σ = (42,000 - 40,000) / 5,000 = 0.4

Using the standard normal distribution table, we find the area to the left of Z = -1.6 is approximately 0.0548 and the area to the left of Z = 0.4 is approximately 0.6554.

To find the percent of salespersons earning between $32,000 and $42,000, we subtract the area to the left of Z = -1.6 from the area to the left of Z = 0.4:

Percent = (0.6554 - 0.0548) * 100% = 60%