The number of surface flaws in plastic panels used in the interior of automobiles has a poisson distribution with a mean of 0.05 flaw 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? (b) if 10 cars are sold to a rental company, what is the probability that none of the 10 cars has any surface flaws? (c) if 10 cars are sold to a rental company, what is the probability that at most one car has any surface flaws?

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Mathematics

Jamison

16 November, 18:57

The number of surface flaws in plastic panels used in the interior of automobiles has a poisson distribution with a mean of 0.05 flaw 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? (b) if 10 cars are sold to a rental company, what is the probability that none of the 10 cars has any surface flaws? (c) if 10 cars are sold to a rental company, what is the probability that at most one car has any surface flaws?

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Dante · Answer 1

Given that the number of surface flaws in plastic panels used in the interior of automobile has a Poisson distribution with a mean of 0.05 flaws per square foot of plastic panel. The number of surface flaws (X) in an automobile interior is also Poisson random variable with a mean of 10 x 0.05 = 0.5. The probability that there are no surface flaws in an auto's interior, P (X = 0) = (e^-0.5 (0.5) ^0 / x!) = e^-0.5 = 0.6065