Question

Medallia calculates and publishes various statistics concerning car quality. The dependability score measures problems experienced during the past 12 months by the owners of vehicles. Toyota had 1.02 problems per car. If you had purchased a Toyota model, what is the probability that in the past 12 months the car had. in excel

Answer 1

Hence the answers are,

a) Probability that in the past 12 months the car had more than one problem = P(X > 1) is 0.2716.

b) The Probability that in the past 12 months the car had almost two problems = P( X < 2) is 0.9160.

c) The Probability that in the past 12 months the car had zero problems = P(X= 0 ) is 0.3606.

Explanation:

Let's take X to be the number of problems per car.

By considering the given statement, X follows a Poisson Distribution with Mean (X) = 1.02.

The Poisson probability formula is :

e Pr( X = k) = e- k! k= 0,1,2...

a)

The Probability that in the past 12 months the car had more than one problem = P(X > 1)

`P(X > 1) =1- P(X < 1) \\\\=1- (P(X = 0) + P(X = 1)-1.021.02 e + 1.021.02 =1-6 0!\\= 1-0.3606 + 0.3678\\= 1-0.7284\\= 0.2716`

b)

The Probability that in the past 12 months the car had almost two problems = PX < 2)

`Pr(X < 2) = Pr(X = i) = Pr(X = 0) + Pr(X = 1) + Pr(X = 2)\\-1.021.020 -1.021.02 -1.021.02 e e + e + 0! 1! 2!\\= 0.3606 + 0.3678 + 0.1876\\= 0.9160`

c)

The Probability that in the past 12 months the car had zero problems = P(X= 0 )

`- 1.021.02 e 0!\\= 0.3606`