SOA Exam P Sample Question 352
Study guide: Exam P-1
A homeowner purchases flood insurance that pays a benefit based on the amount of rain that falls. No benefit is paid for rainfall amounts less than twelve inches. For every full two inches greater than twelve, the insurer pays the homeowner 5000, with a maximum payment of 18,000.
The following table displays probabilities for the rainfall amounts.
Inches of Rain (x) |
Probability of being in interval |
|---|---|
0 \leq x < 2 |
0.04 |
2 \leq x < 4 |
0.06 |
4 \leq x < 6 |
0.07 |
6 \leq x < 8 |
0.09 |
8 \leq x < 10 |
0.12 |
10 \leq x < 12 |
0.14 |
12 \leq x < 14 |
0.18 |
14 \leq x < 16 |
0.11 |
16 \leq x < 18 |
0.08 |
18 \leq x < 20 |
0.07 |
20 \leq x |
0.04 |
Calculate the standard deviation of the benefit paid under the policy.
- A)
2201 - B)
3120 - C)
3200 - D)
5452 - E)
5680
Answer this question and see the worked solution
Concepts tested
- Variance and Standard Deviation
- Discrete Univariate Distributions
- Payment Random Variable
- Expected Value