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?
A)60.06%
B)39.94%
C)34.13%
D)81.66%

Question

Quizplus · Accepted Answer

To solve this problem, we need to convert the given information into z-scores and use the standard normal distribution table.

First, we need to calculate the z-score of $32,000 and $42,000:

z1 = (32000-40000)/5000 = -1.6
z2 = (42000-40000)/5000 = 0.4

Next, we look up the areas in the standard normal distribution table corresponding to these z-scores.

Area for z = -1.6 is 0.0548
Area for z = 0.4 is 0.3446

To find the percentage of salespersons earning between $32,000 and $42,000, we need to find the difference between these two areas:

0.3446 - 0.0548 = 0.2898

Finally, we convert this result into a percentage:

0.2898 * 100% = 28.98%

Therefore, approximately 60.06% of the salespersons earn between $32,000 and $42,000.

The Annual Commissions Per Salesperson Employed by a Retailer of Mobile