Question

The number of surface flaws in a plastic roll used for auto interiors follows a Poisson distribution with a mean of 0.05 flaw per square foot . Each car contains 10 ft2 of the plastic roll and ten (10) of the cars are sold to a particular rental agency. a) What is the probability that there are no flaws in a given car’s interior

Answer 1

Answer:

0.6065

Step-by-step explanation:

Probability mass function of probability distribution : $P(X=x)=\frac{e^{-\lambda} \times \lambda^x}{x !}$

a mean of 0.05 flaw per square foot

Each car contains 10 sq.feet of the plastic roll

Mean = 0.05

Mean = $\lambda = 0.05 \times 10=0.5$

We are supposed to find What is the probability that there are no flaws in a given car’s interior i.e,P(X=0)

Substitute the value in the formula

$P(X=0)=\frac{e^{-0.5} \times (0.5)^0x}{0 !}$

$P(X=0)=\frac{e^{-0.5} \times (0.5)^0}{1}$

$P(X=0)=0.6065$

Hence the probability that there are no flaws in a given car’s interior is 0.6065