Concept explainers
An auditor for Health Maintenance Services of Georgia reports 40% of policyholders 55 years or older submit a claim during the year. Fifteen policyholders are randomly selected for company records.
- a. How many of the policyholders would you expect to have filed a claim within the last year?
- b. What is the probability that 10 of the selected policyholders submitted a claim last year?
- c. What is the probability that 10 or more of the selected policyholders submitted a claim last year?
- d. What is the probability that more than 10 of the selected policyholders submitted a claim last year?
a.
Find the number of policyholders who are expected to have filed a claim within the last year.
Answer to Problem 45CE
The number of policyholders who are expected to have filed a claim within the last year is 6.
Explanation of Solution
The number of policyholders who are expected to have filed a claim within the last year is calculated as follows:
Therefore, the number of policyholders who are expected to have filed a claim within the last year is 6.
b.
Calculate the probability that 10 of the selected policyholders submitted a claim last year.
Answer to Problem 45CE
The probability that 10 of the selected policyholders submitted a claim last year is 0.0245.
Explanation of Solution
The formula to find the binomial probability is as follows:
Here, n=15 and π=0.40.
The probability that 10 of the selected policyholders submitted a claim last year is calculated as follows:
Therefore, the probability that 10 of the selected policyholders submitted a claim last year is 0.0245.
c.
Calculate the probability that 10 or more of the selected policyholders submitted a claim last year.
Answer to Problem 45CE
The probability that 10 or more of the selected policyholders submitted a claim last year is 0.0338.
Explanation of Solution
The probability that 10 or more of the selected policyholders submitted a claim last year is calculated as follows:
Therefore, the probability that 10 or more of the selected policyholders submitted a claim last year is 0.0338.
d.
Calculate the probability that more than 10 of the selected policyholders submitted a claim last year.
Answer to Problem 45CE
The probability that more than 10 of the selected policyholders submitted a claim last year is 0.0093.
Explanation of Solution
The probability that more than 10 of the selected policyholders submitted a claim last year is calculated as follows:
Therefore, the probability that more than 10 of the selected policyholders submitted a claim last year is 0.0093.
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Chapter 6 Solutions
Loose Leaf for Statistical Techniques in Business and Economics
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