Salespeople of a large corporation received an annual bonus based on their sales performance. The size of the bonuses was normally distributed with a mean of $$11,000$ and a standard deviation of $$2400.$ Complete parts $($a$)$ through $($d$)$ below.

Click here for page $1$ of the Areas under the Normal Curve Table Click he

$79\mathrm{.}67\%$ of the salespeople

$($Round to the nearest hundredth as needed.$)$

$($b$)$ What percent of the salespeople received an annual bonus between $$9000$ and $$13,800?$

$67\mathrm{.}57\%$ of the salespeople

$($Round to the nearest hundredth as needed.$)$

d$)$ Find the largest and smallest amounts for the middle $75\%$ of the annual bonuses.

The smallest amount is $ and the largest amount is $

$($Round to the nearest dollar as needed. Do not include the $ symbol in your answer.$)$

POSITIVE z Scores

TABLE A$-2($continued$)$ Cumulative Area from the LEFT

NEGATIVE z Scores

TABLE A$-2$ Standard Normal $(z)$ Distribution: Cumulative Area from the LEFT

"Use these common values that result from interpolation:

$\backslash$table$[[z$ Score,Area$],[-1\mathrm{.}645,0\mathrm{.}0500],[-2\mathrm{.}575,0\mathrm{.}0050]]$