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}*1.08^{0}/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=0}^{a }
(_{n}C_{x})p^{x}(1−p)^{(n-x) }
= |
0.0395 |

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