Concept explainers
(a)
To construct: a probability model for the gain on a policy.
(a)
Explanation of Solution
Given:
Price of the insurance policy = $100.
When a major injury happens, the amount paid by the insurance provider to the purchaser is $10,000. When a minor injury happens, the amount paid by the insurance provider to the purchaser is $3,000. The company calculates that every year 1 in every 2000 might have a major injury. The company calculates that every year 1 in every 500 might have a minor injury.
Calculation:
The probability a policyholder
For the major injury Is,
For minor injury is
The probability that company would have gain is,
Let X be the gain of the company.
Price of the Insurance policy is $100.
If the policyholder is major hurt, the amount the organization would recover from is,
If the policyholder is minor hurt, the amount the organization would recover from is
the probability distribution of gain on the policy is,
Type | X($) | P(X=x) |
Major injury | -9900 | 0.0005 |
Minor injury | -2900 | 0.0020 |
Profit | 100 | 0.9975 |
Total | 1 |
(b)
To find: the company’s predicted gain on this policy.
(b)
Answer to Problem 18E
$89
Explanation of Solution
Given:
From the part (a)
the probability distribution of gain on the policy is,
Type | X($) | P(X=x) |
Major injury | -9900 | 0.0005 |
Minor injury | -2900 | 0.0020 |
Profit | 100 | 0.9975 |
Total | 1 |
Formula used:
Calculation:
Expected gain is
Therefore, the company’s predicted gain on the policy is $89.
(c)
To Calculate: the standard deviation.
(c)
Answer to Problem 18E
260.536
Explanation of Solution
Given:
From the part (a)
the probability distribution of gain on the policy is,
Type | X($) | P(X=x) |
Major injury | -9900 | 0.0005 |
Minor injury | -2900 | 0.0020 |
Profit | 100 | 0.9975 |
Total | 1 |
Formula used:
Calculation:
Estimating the standard deviation.
The variance
The standard deviation
Thus, the standard deviation of the gain on a policy is 260.536.
Chapter 16 Solutions
Stats: Modeling the World Nasta Edition Grades 9-12
Additional Math Textbook Solutions
Elementary Statistics
Fundamentals of Statistics (5th Edition)
Introductory Statistics
Statistics for Business and Economics (13th Edition)
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