The number of surface flaws in plastic panels used in the in

The number of surface flaws in plastic panels used in the interior of automobiles has a Poisson distribution with a mean of 0.06 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?

(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?

Round your answers to four decimal places (e.g. 98.7654).

Solution

The probability distribution of a Poisson random variable X representing the number of successes occurring in a given time interval or a specified region of space is given by the formula: <?xml:namespace prefix = o ns = \"urn:schemas-microsoft-com:office:office\" /?>

P(X)=[{(e)^(??)} *{(?)^x}]/x!

where

x=0,1,2,3...

e=2.71828 (but use your calculator\'s e button)

`? =` mean number of successes in the given time interval or region of space

The number of surface flaws in plastic panels used in the interior of automobiles has a Poisson distribution with a mean of 0.03 flaws per square foot of plastic panel. Assume an automobile interior contains 10 square feet of plastic panel.

So mean number of flaws= ? = 0.03*10 = 0.3

(a) What is the probability that there are no surface flaws in an auto\'s interior?

P(0) = [{(2.71828)^(?0.3)} *{(0.3)^0}]/0!= 0.7408

(b) If 10 cars are sold to a rental company, what is the probability that none of the 10 cars has any surface flaws?

If 10 cars are there, mean no. of flaws, ? = 10* 0.3 = 3

P(0) = [{(2.71828)^(?3)} *{(3)^0}]/0!= 0.0498

(c) If 10 cars are sold to a rental company, what is the probability that at most one car has any surface flaws= P(0)+P(1)

P(1) = probability that one of the 10 cars has surface flaws

= [{(2.71828)^(?3)} *{(3)^1}]/1!= 0.1494

Hence, probability that at most one car has any surface flaws= 0.0498+ 0.1494 = 0.1992