Probability Distributions Problem Set
Solutions are provided at the end of the document
P1 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 






 What is the probability of selling 5 houses in a month?
 What are the expected value and the standard deviation for the number houses sold by the salespeople per month?
P2 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.
P3 Forty 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
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