Question

In Hawaii, the rate of motor vehicle theft is 707 thefts per 100,000 vehicles. A large parking structure in Honolulu has issued 596 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 four or more vehicles with a permit will eventually be stolen? (Use 4 decimal places.)

Answer 1

Here

707 thefts per 100000

p = 707/ 100000 = 0.00707

A large parking structure issued 596 parking permits, n = 596

Mean = np = 596 * 0.00707 = 4.21372 ~ 4.2

Poisson distribution

a)

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

P(X=0) = 0.0150

b)

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

P(X>=1) = 0.9850

c)

The probability that four or more vehicles with a permit will eventually be stolen

P(X>=4) = 0.6046