A company publishes statistics concerning car quality The in

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 1.22 problems per car. Let the random variable X be equal to the number of problems with a newly purchased model A car. Complete (a) and (b) below. Round to four decimal places as needed for both answers.

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

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

Solution

This is a Poisson Process.

Note that,

P(x) = u^x e^(-u)/x!

where x = number of successes
u = mean = 1.22.

a)

Plugging in x = 0,

P(0) = 0.295230167
[answer]

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b)

Note that

P(2 or fewer) = P(2) + P(1) + P(0)

Plugging in x= 1,

P(1) = 0.360180804

Plugging in x = 2,

P(2) = 0.295230167

Thus,

P(2 or fewer) = 0.875121261 [ANSWER]