Chapter 8.2, Problem 23E

EXPECTED HOME SALES OF A REALTOR Sally Leonard, a real estate broker, is relocating in a large metropolitan area where she has received job offers from Realty Company A and Realty Company B. The number of houses she expects to sell in a year at each firm and the associated probabilities are shown in the following tables:

Company A:

Houses Sold	$12$	$13$	$14$	$15$	$16$	$17$	$18$	$19$	$20$	$21$	$22$	$23$	$24$
Probability	$.02$	$.03$	$.05$	$.07$	$.07$	$.16$	$.17$	$.13$	$.11$	$.09$	$.06$	$.03$	$.01$

Company B:

Houses Sold	$6$	$7$	$8$	$9$	$10$	$11$	$12$	$13$	$14$	$15$	$16$	$17$	$18$
Probability	$.01$	$.04$	$.07$	$.06$	$.11$	$.12$	$.19$	$.17$	$.13$	$.04$	$.03$	$.02$	$.01$

The average price of a house in the locale of Company A is $\$308,000$, whereas the average price of a house in the locale of Company B is $\$474,000$. If Sally will receive a $3\%$ com-mission on sales at either company, which job offer should she accept to maximize her expected yearly commission?