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# Probability and Frequencies

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Banner Mattress and Furniture Company
The Banner Mattress and Furniture Company wishes to study the number of credit applications received per day for the last 300 days. The information is reported below:

Number of Credit Frequency
Applications (Number of Days)

0 50
1 77
2 81
3 48
4 31
5 or more 13

To interpret, there were 50 days on which no credit applications were received, 77 days on which only one application was received, and so on. Would it be reasonable to conclude that the population distribution is Poisson with a mean of 2.0? Use the .05 significance level. Hint: To find the expected frequencies use the Poisson distribution with a mean of 2.0. Find the probability of exactly one success given a Poisson distribution with a mean of 2.0. Multiply this probability by 300 to find the expected frequency for the number of days in which there was exactly one application. Determine the expected frequency for the other days in a similar manner.

#### Solution Summary

Fully formatted solution contains step-by-step explanation on how to solve the problem using a chi-square test.

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## Probability Frequency Definition

2. The table below represents the results of a survey of 1000 workers in Q1 2009 as to which benefit they find is the most important.

Retirement
Benefits are most important Health Benefits are most important
Single 280 200
Married 220 300

a. If a Worker is chosen at random, what is the probability that he/she feels health benefits are most important?

b. If a Voter is chosen at random, what is the probability that he/she is married?

c. If a Voter is chosen at random, what is the probability that he/she is married and feels Health benefits are most important?

d. Given that a worker is single, what is the probability that he/she feels retirement benefits are most important?

e. Given that a worker feels Health benefits are most important, what is the probability that he/she is married?

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