Question

In Hawaii, the rate of motor vehicle theft is 503 thefts per 100,000 vehicles. A large parking structure in Honolulu has issued 491 parking permits.

(a) What is the probability that none of the vehicles with a permit will eventually be stolen? (Round λ to 1 decimal place. Use 4 decimal places for your answer.)

(b) What is the probability that at least one of the vehicles with a permit will eventually be stolen? (Use 4 decimal places.)

(c) What is the probability that three or more vehicles with a permit will eventually be stolen? (Use 4 decimal places.)

Answer 1

(a)

Poisson Distribution.

Mean = = np = 435 X 0.00486 = 2.1

Probability Mass Function of X is given by:

                                     for x = 0, 1,..

For X = 0:

So,

the probability that none of the vehicles with a permit will eventually be stolen = 0.1225

(b)

P(X1) = 1- P(X=0) = 1- 0.1225 = 0.8775

So,

So,

the probability that at least one of the vehicles with a permit will eventually be stolen = 0.8775

(c)

P(X3) = 1 - [P(X=0) + P(X=1) + P(X=2)]

So,

P(X3) = 1 - 0.6496=0.3504

So,

So,

the probability that three or more vehicles with a permit will eventually be stolen = 0.3504