Question

J.D. power and Associates calculates and publishes various statistics concerning car quality. The dependability score measures problems experienced during the past 12 months by original owners of three-year-old vehicles (those that were introduced for the 2017 model year). For these models of cars, Ford had 1.27 problems per car and Toyota had 1.12 problems per car. (Data extracted from 2013 U.S. Vehicle Dependability Study,J.D. Power and Associates, February 13, 2013, Let X be equal to the number of problems with a three -year -old Ford.

a. What assumptions must be made in order for X to be distributed as a Poisson random variable? Are these assumptions reasonable? Making the assumptions as in (a), if you purchased a Ford in the 2010 model year, what is the probability that in the past 12 months, the car had
b. zero problems?
c. two or fewer problems?
d. Give an operational definition for problem. Why is the operational definition important in interpreting the initial quality score?

Answer 1

0.281 ; 0.864

Explanation:

1.)

p decreases as n increases (n increases, p--> 0)

λ ≥ 0

P(x = x) = (e^-λ * λ^x) ÷ x!

λ for Ford = 1.27

B) zero problems :

P(x = 0) :

(e^-1.27 * 1.27^0) ÷ 0! = 0.281

P(x = 0) = 0.281

Two or fewer problems :

P(x ≤ 2) = p(x = 0) + p(x = 1) + p(x = 2)

P(x ≤ 2) = 0.281 + 0.357 + 0.226

P(x ≤ 2) = 0.864

D.) It allows for early detection and thus adequate curtailment of the problem at an a stage in which it seems easier to curb.