Question

The number of surface flaws in a plastic roll used in the interior of automobiles has a Poisson distribution with a mean of 0.09 flaw per square foot of plastic roll. Assume an automobile interior contains 12 square feet of plastic roll. Round your answers to four decimal places (e.g. 98.7654).

(a) What is the probability that there are no surface flaws in an auto’s interior?
(b) If 17 cars are sold to a rental company, what is the probability that none of the 17 cars has any surface flaws?
(c) If 17 cars are sold to a rental company, what is the probability that at most 2 cars has any surface flaws?

Answer 1

a)Poisson

expected number of flaws in an auto’s interior =12*0.09 =1.08

from Poisson distribution:

probability that there are no surface flaws in an auto’s interior =e^-1.08*1.08⁰/0! =0.3396

b)

here this is binomial with parameter n=17 and p=0.3396

probability that none of the 17 cars has any surface flaws =0.3396^17=0.0009

c)

probability that at most 2 cars has any surface flaws :

P(X<=2)=

∑x=0a     (nCx)px(1−p)(n-x)    =

0.0395