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

$581,500

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}`