An insurance company has 1,000 policies on men of age 50. The company estimates that the probability that a man of age 50 dies within a year is .01. Estimate the number of claims that the company can expect from beneficiaries of these men within a year.

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Answer:

the expected number of claims within a year is 10

Step-by-step explanation:

since the life expectancy of each man is independent from others, then the random variable X= number of man of 50 years who die within a year , follows a binomial distribution. Thus the expected value of X is given by

E(X) = n*p

where

p= probability that a man of age 50 dies within a year = 0.01

n = number of policies on men of age 50 = 1000

replacing values

E(X) = n*p = 0.01 * 1000 = 10

therefore the expected number of claims within a year is 10

Using the binomial distribution, it is found that the estimate of the number of claims that the company can expect from beneficiaries of these men within a year is of 10.

For each men, there are only two possible outcomes, either there is a claim(they die), or there is not a claim. The probability of a men dying is independent of any other men, hence, the binomial distribution is used to solve this question.

Binomial probability distribution

Probability of exactly x successes on n repeated trials, with p probability, and has expected value given by:

[tex]E(X) = np[/tex]

In this problem:

  • There are 1000 policies, hence [tex]n = 1000[/tex].
  • Each of them has a 0.01 probability of dying, hence causing a claim, which means that [tex]p = 0.01[/tex].

Then:

[tex]E(X) = 1000(0.1) = 10[/tex]

The expected number of claims is of 10.

To learn more about the binomial distribution, you can take a look at https://brainly.com/question/25642476

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