Question

A company publishes statistics concerning car quality. The initial quality score measures the number of problems per new car sold. For one​ year, Car A had .79 problems per car and car B had .26 problems per car. Let the random variable X be equal to the number of problems with a newly purchased model A car. Complete​ (a) through​ (c) below

If you purchased a model A​ car, what is the probability that the new car will have zero​ problems?

If you purchased a model A​ car, what is the probability that the new car will have two or fewer​ problems?

Compare your answers in​ (a) and​ (b) to those for car B.

Because Car B has a (Higher/lower) mean rate of problems per car than Car​ A, the probability of a randomly selected Car B having zero problems and the probability of no more than two problems are both (higher/lower) than for Car A.

Answer 1

Using Poisson distribution

Let X be the number of probalems per car of model A

Then X follow Poisson with

The probability mass function of X is

, x= 0,1,2,....

= 0.9540

Probability that new car of model A has zero problems = 0.4538

Probability that new car of model A has 2 or fewer problems = 0.9540

Let Y be the number of probalems per car of model B

Then Y follow Poisson with

The probability mass function of Y is

, y= 0,1,2,....

= 0.9976

Probability that new car of model B has zero problems = 0.7711

Probability that new car of model B has 2 or fewer problems = 0.9976

Comaprison

Car B (0.26)has a LOWER mean rate of problems per car than car A(0.79) , probability that a randomly selected car B has zero problems and the probability of no more than 2 problems are both HIGHER  than for car A .

Note : Probability that new car of model B has zero problems > Probability that new car of model A has zero problems

Probability that new car of model B has 2 or fewer problems > Probability that new car of model A has 2 or fewer problems