Death Claims

[rad6210]

A University is considering giving life insurance coverage to all students in good standing. To test this idea, the university decides to insure for one year all students who will be both 20 years old and in good standing on January 1, 2010 (that is, the insurance will expire on January 1, 2011). The insurance provides for a payment of 1 unit to the student’s beneficiary only if the student dies during the year. Assume that the probability of death during the year for each student is given by the value of q20 in the U.S. Life Table in Chapter 3. If the university sets aside 12.33 units to cover 7,148 students, what is the probability that there will be enough money to pay all the death claims? (Use the normal approximation.) (Answer: 90%)

I know you obviously don't have the US Life Table, but if anyone knows how to just set this up it would be really helpful! Thank you!

 

[tkhunny]

Who doesn't have the U.S. Life Table from Chapter 3?!

#1 - There is a massive over-simplification with this problem. Your teacher should be impressed if you point this out. There is no way you can demonstrate the independence of your students' deaths. They go to the same school and they hang out together. They take long, foolish drives together. These lives are absolutely NOT independent.

#2 - Having said that, let's assume the students' live are independent...

Mean = 7148*q20 -- You should recognize this as the mean of a binomial distribution - mean number of deaths.
Variance = 7148*q20*p20 -- You should recognize this as the Variance of a binomial distribution.

Your Normal approximation should be a piece of cake from there.