Question

In: Statistics and Probability

2. Jenni is an insurance agent for the company listed in question 1. The number of...

2. Jenni is an insurance agent for the company listed in question 1. The number of whole-life policies she has written (sold) that lapse is Poisson distributed with a mean of 12 policies per year.

a. What is the probability only 9 of Jenni’s whole-life policies will lapse in a given year? (1 point)

b. What is the probability 16 of Jenni’s whole-life policies will lapse in a given year? (1 point)

Question 1 (for reference)

  1. An insurance company is concerned about the persistency (length of time a policy remains in-force and doesn’t lapse) of its whole-life policies. Suppose the persistency of the company’s whole-life policies is normally distributed with a mean of 13 years and a standard deviation of 4 years.

a. What is the probability that the persistency of a whole-life policy will be less than 10 years? (1 point)

Answer to A: .2266

b. If the insurance company wants no more than 5% of its whole-life policies to have a persistency of less than 8 years, what does its mean persistency need to be? (Assume the same standard deviation) (1 point)

Answer to B: Mean= 14.5794

Solutions

Expert Solution

2:

Let Y is a random variable shows the number of whole-life policies lapse per year. Here Y has Poisson distribution with parameter . The requried pdf is

(a)

The probability only 9 of Jenni’s whole-life policies will lapse in a given year is

(b)

The probability 16 of Jenni’s whole-life policies will lapse in a given year is

-----------------------------------------------------

(a)

Let X is a random variable shows that persistency of a whole-life policy. Given that

(b)

We need to find such that

P(X < 8) = 0.05

The requried population mean is

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orchestra answered 2 years ago
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