Question

In: Statistics and Probability

Assume that past 100 years of data revealed that 20 tornadoes occurred in a county. Further...

Assume that past 100 years of data revealed that 20 tornadoes occurred in a county. Further assume that the wind speed due to tornadoes can be modeled by a normal random variable with a mean of 130 mph and a standard deviation of 13 mph.

(a) Calculate the probability that there will be at least two tornadoes next year?

(b) Suppose a building in the county is designed for wind speed of 150 mph. Calculate the probability that the building will be damaged during such a tornado?

(c) What is the probability that the building in part (b) will be damaged by tornado next year?

Expert Solution

a) The probability that there will be at least two tornadoes next year is computed here as:

= 1 - Probability that there would be 0 or 1 tornado in the next year

Therefore 0.0175 is the required probability here.

b) The probability that the building will be damaged is computed here as:
P(X > 150) where X is the random variable representing the wind speed here.

Converting it to a standard normal variable, we have here:

Getting it from the standard normal tables, we have here:

Therefore 0.0620 is the required probability here.

c) The probability that the building in part b) will be damaged by a tornado next year is computed here as:
= 1 - Probability that it wont be damaged

= 1 - P(N = 0) - P(N = 1)*0.0620 - P(N = 1)*0.0620² - ..... Infinity

The part of the above equation after 1 is a sum of a poisson distribution with parameter 0.0620*0.2.

Therefore 0.1711 is the required probability here.

orchestra answered 2 years ago

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