The number of surface flaws in plastic panels used in the interior of automobiles has a Poisson distribution with a mean of 0.08 flaws per square foot of plastic panel. Assume an automobile interior contains 10 square feet of plastic panel. (a) What is the probability that there are no surface flaws in an auto's interior

(a) Probability that there are no surface flaws in an auto's interior is 0.4493 .

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 0.08 flaws per square foot of plastic panel.

Let X = Distribution of number of surface flaws in plastic panels

So, X ~ Poisson()

The mean of Poisson distribution is given by, E(X) = = 0.08

which means, X ~ Poisson(0.08)

The probability distribution function of a Poisson random variable is:

Now, we know that for per square foot of plastic panel is 0.08 and we are given that an automobile interior contains 10 square feet of plastic panel.

Therefore, for 10 square foot of plastic panel is = 10 * 0.08 = 0.8

(a) Probability that there are no surface flaws in an auto's interior =P(X=0)

    P(X = 0) = = = 0.4493

answer:  

step-by-step explanation:

here x represents the height of the pole,

and, the height of the shadow of the pole is 12 feet.

also, the angle of elevation from the top of the pole is 40°,

therefore,

by the low of sine,

which is the required equation for finding the value of x,