A company publishes statistics concerning car quality. The initial quality score

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 1.31 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. 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? Round to four decimal places as needed.

Explanation / Answer

Ans:

Poisson distribution with mean=1.31

a)P(x=0)=e-1.31*(1.310/0!)=e-1.31=0.2698

b)P(x<=2)=e-1.31*(1.310/0!+1.311/1!+1.312/2!)

=e-1.31*(1+1.31+0.8581)

=e-1.31*3.1681

=0.8548

or using excel function:

P(x<=2)=POISSON(2,1.31,TRUE)=0.8548

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