Question

Suppose a company has several hundred sales people on its staff nationwide. Last year, the total annual sales per salesperson was normally distributed with a mean of $550,000 and a standard deviation of $35,000. If your friend was a sales man for this company, and his sales total for the year was -0.9 standard deviations below the mean. How much did he sell?

Answer 1

Answer:

$581,500

Step-by-step explanation:

Let $\large \mu$ = $550,000 the annual sales mean and $\large \sigma$ = $35,000 the standard deviation.

If your friend's  sales total for the year were 0.9 standard deviations below the mean, then he would have sold

$\large \mu-0.9\sigma=550,000-(0.9)35,000=550,000-0.9*35,000=\ 518,500$

But, he sold minus 0.9 standard deviations below the mean, so he really sold

$\large \mu-(-0.9)\sigma=550,000-(-0.9)35,000=550,000+0.9*35,000=\\=\boxed{\ 581,500}$