ProbabilityDistributions Problem Set

Solutions are provided at the end of the document

P-1 The salespeople at Owl Realty sell up to 9 houses per month. The probability distribution of a salesperson selling n houses in a month is as follows:
Sales
Probability

0
.05

1
.10

2
.15

3
.20

4
.15

5

6
.10

7
.05

8
.05

9
.05

a. What is the probability of selling 5 houses in a month?
b. What are the expected value and the standard deviation for the number houses sold by the salespeople per month?

P-2 The following data has been recorded regarding the rental history of a high pressure cleaner at a home improvement store.
Demand
Frequency

0
20

1
23

2
27

3
14

4
16

Find the expected demand for the high pressure cleaner.

P-3Forty percent of all high school graduate work during the summer to earn money for college tuition for the upcoming fall term. Assuming a binomial distribution, if 6 graduates are selected at random, what is the probability that:
a) 3 have a summer job
b) None have a summer job
c) All have a summer job
d) At least 2 have a summer job