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

1.491.49 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.

b.

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

The probability that a new model A car will have two or fewer problems is ___ .

(Round to four decimal places as needed.)

Solution

Possion Distribution
PMF of P.D is = f ( k ) = e- x / x!
Where   
= parameter of the distribution.
x = is the number of independent trials
P( X < = 2) = P(X=2) + P(X=1) + P(X=0)   
= e^-1.49 * 1.49 ^ 2 / 2! + e^-1.49 * 10 ^ 1 / 1! + e^-1.49 * ^ 0 / 0!
= 0.8114