Question

5. A company prices its tornado insurance using the following assumptions: • In any calendar year, there can be at most one tornado. • In any calendar year, the probability of a tornado is 0.14. • The number of tornadoes in any calendar year is independent of the number of tornados in any other calendar year. Using the company's assumptions, calculate the probability that there are fewer than 3 tornadoes in a 10-year period.

Answer 1

Let x be  number of Tornados

probability of a tornado p = 0.03

n = 10

here, trials are independent and fixed also there are only two possible outcomes with success probability is 0.14

so we can use binomial distribution to find the probability.

here we want to find P( X < 3) = P( X < = 3-1) = P(X <=2)

Using excel:

Note the general command to find less than or equal binomial probability in excel is "=BINOMDIST(x, n, p, 1)"

therefore P( X <=2) = "BINOMDIST(2,10,0.14,1)" =0.845470175

So  the probability that there are fewer than 3 tornadoes in a 10-year period is 0.845470175