Suppose you work for a car insurance company that covers about 200,000 drivers i

Question

Suppose you work for a car insurance company that covers about 200,000 drivers in New Hampshire. The company estimates that about 14% of people in the state will be involved in a car accident over the next year.

What is the expected number of drivers covered by your company who will be involved in a car accident?

What is the variance of the number of people your company covers who will be involved in car accidents?

Suppose, however, that of those 200,000 drivers you cover, 2,500 are aged 16 – 18, a group for which 18% of drivers will be in an accident in a given year. How many accidents involving 16 – 18 year old drivers would you expect to occur?

Find the probability that someone aged 19 or older will be involved in an accident. (Hint: You can easily find both the number of such drivers your company covers, and the expected value, based on parts A and C).

Explanation / Answer

p = 0.14
n = 200,000

A.
expected number = np = 200000 * 0.14 = 28000

B.
Variance = np(1-p) = 200000 * 0.14 * 0.86 = 24080

C.
Now, for the age group 16-18
n = 2500
p = 0.18
Expected accidents = np = 2500*0.18 = 450

D.
expected number of accidents for the age of 19 and above = 28000 - 450 = 27550

number of people covered 19 and above is 200000 - 2500 = 197500

probability = 27550/197500 = 0.1395

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