Question

Let X be the number of houses that an agent sold in a day. Suppose X has the following probability mass function (pmf):

y	0	1	2	3
p(y)	0.5	0.33	0.14	0.03

The agent receives a 900-dollar commission for each sale made. On top of any applicable commission, there is a 600-dollar bonus pay if the agent makes at least 3 sales in a day.

Answer the following questions.

(a) If the agent makes at least one sale, what is the probability that the agent would receive the bonus pay? In other words, what is P(X = 3 | X ≥ 1)? If necessary, round your answer to four decimal places.

P(X = 3 | X ≥ 1) =

(b) How many sales do you expect the agent to make in one day? If necessary, round your answer to two decimal places.

sales

(c) Assuming there is no other pay available, how much money do you expect the agent to make in one day? If necessary, round your answer to the nearest whole number.

dollars

Answer 1

Given

x	P(x)
0	0.5
1	0.33
2	0.14
3	0.03

(b)

Number of sales the agent expected to make in one day = E(X)

Number of sales the agent expected to make in one day = 0.7

sales = 0.7

(c)

The agent receives a 900-dollar commission for each sale made.

Amount of money the agent is expected to make in one day

= 900 x Number of sales the agent expected to make in one day = 900 x 0.7 = 630

Amount of money the agent is expected to make in one day = $630

dollors = 630