# STATS – A probability distribution for the claim sizes for an auto insurance policy

August 30, 2017

Question
A probability distribution for the claim sizes for an auto insurance policy is given in the table below

Claim Size 20
30
40

50 60 70 80

Probability 0.20
0.10
0.10

0.20 0.15 0.10 0.15

a) Evaluate the cdf for this distribution at the following points: 0, 20, 30, 40, 50, 90.

8. Airtran’s flight #307 can accomodate 50 passengers, but the flight is over- booked, as 52 tickets were sold. Each ticketed passenger can arrive late and miss the flight with a probability 0.02. What is the probability that no passenger arrives late? What is the probability that exactly one passanger arrives late? What is the probability that Airtran has to pay overbooking fees (and reschedule passengers to different flights)?

9. The world incidence of (frequency of world population having) diabetes is 5%. If 20 persons are chosen at random, what is the probability that no more than 3 have the disease?

10. Plot in Excel the probability mass function (density) for the following:

• a Binomial random variable X with n = 10, p = 0.3 • a Binomial random variable Y with n = 100, p = 0.4 • a Uniform random variable X with n = 50

Attach the clearly labeled graphs.

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