Question

A particular term life insurance offers death and disability benefits to any senior citizen. There is a 10% probability that the policy holder will die in the next 20 years and there is a 80% probability that the policy holder will be disabled. The policy pays US$300 for death and $25 for disability. If neither death nor disability happens, the insurance company pays nothing. Use this information to answer the following questions. Use two decimals.

1. What formula would you use to find the standard deviation of the probability distribution in the given context?

2. What is the sum of the P(x) values of the probability distribution in the given context?

3. Based on the given information above, what is the variance?

4. How many P(x) values are there to find the mean of the probability distribution in the given context?

5. What formula would you use to find the variance of the probability distribution in the given context?

6. How many x values are there to find the mean of the probability distribution in the given context?

7. What is the sum of the product of the x and P(x) value in calculating the mean of the probability distribution in the given context?

8. Based on the given information above, what is the sum of the differences squared (x-mean)^2?

9. List the P(x) values to find the mean of the probability distribution in the given context?

10. Based on the given information above, what is the sum of the product of the differences squared (x-mean)^2 and P(x)?

11. What is the sum of the x values of the probability distribution in the given context?

12. What does it mean to have a positive mean (expected value) from the point of the insurance company?

13. What does it mean to have a negative mean (expected value) from the point of the insurance company?

14. Based on the given information above, what is the expected value?

15. List the x values to find the mean of the probability distribution in the given context?

16. Based on the given information above, what is the sum of the differences(x-mean)?

17. What formula would you use to find the mean of the probability distribution in the given context?

18. How do you use the variance to find the standard deviation?

19. Based on the given information above, what is the standard deviation?

20. Interpret the mean(expected value) of the distribution in the context of the question?

Answer 1

1. The formula to find the standard deviation of the probability distribution is: square root of variance.

2.The sum of the P(x) values of the probability distribution is 1.

3. The variance is ((0.1*300-expected value)^2)0.9 + ((0.825-expected value)^2)*0.2.

4. There are two P(x) values to find the mean of the probability distribution in the given context.

5. The formula to find the variance of the probability distribution is: ∑ (x-expected value)^2 * P(x).

6. There are two x values to find the mean of the probability distribution in the given context.

7. The sum of the product of the x and P(x) value in calculating the mean of the probability distribution is (0.1300) + (0.825).

8. The sum of the differences squared (x-mean)^2 is ((300-mean)^2)*0.1 + ((25-mean)^2)*0.8.

9. The P(x) values to find the mean of the probability distribution are 0.1 and 0.8.

10. The sum of the product of the differences squared (x-mean)^2 and P(x) is ((300-mean)^2)*0.1 + ((25-mean)^2)*0.8.

11. The sum of the x values of the probability distribution is (0.1300) + (0.825).

12. A positive mean (expected value) means that on average, the insurance company can expect to receive a profit from the policy over time.

13. A negative mean (expected value) means that on average, the insurance company can expect to incur a loss from the policy over time.

14. The expected value is (0.1300) + (0.825) = $41.

15. The x values to find the mean of the probability distribution are $300 and $25.

16. The sum of the differences (x-mean) is (300-mean)*0.1 + (25-mean)*0.8.

17. The formula to find the mean of the probability distribution is: ∑ x * P(x).

18. The standard deviation is the square root of the variance.

19. The standard deviation is the square root of (((300-mean)^2)*0.1 + ((25-mean)^2)*0.8).

20. The mean (expected value) of the distribution indicates the average profit or loss the insurance company can expect from the policy over time. In this context, the expected value of $41 suggests that on average, the insurance company can expect to make a profit from this particular policy