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 8 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 15 cars are sold to a rental company, what is the probability that none of the 15 cars has any surface flaws? (c) If 15 cars are sold to a rental company, what is the probability that at most 2 cars has any surface flaws ?

Answer 1

Given

p= 0.09

n= 8

=np =0.09*8 = 0.72

P(x)=

The probability that there are no surface flaws in an auto’s interior=

P(x=0) =    = 0.4868 Answer

  When there are 15 cars then total square feet of plastic =15*8 =120 square feet

now n=120

so =np =0.09*120 = 10.8

The probability that none of the 15 cars has any surface flaws=

2.0399* 10-5  = 0.0000204

=0.0000 Answer

The probability that at most 2 cars has any surface flaws = P(x=0) +P(x=1) + P(x=2)

=

= 0.001430413

= 0.0014 Answer