Respuesta :
Answer:
(a) Probability that there are no surface flaws in an auto's interior is 0.6703 .
Step-by-step explanation:
We are given that the number of surface flaws in plastic panels used in the interior of automobiles has a Poisson distribution with a mean of 0.04 flaws per square foot of plastic panel.
Let X = Distribution of number of surface flaws in plastic panels
So, X ~ Poisson([tex]\lambda[/tex])
The mean of Poisson distribution is given by, E(X) = [tex]\lambda[/tex] = 0.04
which means, X ~ Poisson(0.04)
The probability distribution function of a Poisson random variable is:
[tex]P(X=x)=\frac{e^{-\lambda}\lambda^{x}}{x!}; for x=0,1,2,3...[/tex]
Now, we know that [tex]\lambda[/tex] for per square foot of plastic panel is 0.04 and we are given that an automobile interior contains 10 square feet of plastic panel.
Therefore, [tex]\lambda[/tex] for 10 square foot of plastic panel is = 10 * 0.04 = 0.4
(a) Probability that there are no surface flaws in an auto's interior =P(X=0)
P(X = 0) = [tex]\frac{e^{-0.4}*0.4^{0}}{0!}[/tex] = [tex]e^{-0.4}[/tex] = 0.6703
