A certain kind of sheet metal has an average of 9 defects per 13 ft2. Assuming a

Question

A certain kind of sheet metal has an average of 9 defects per 13 ft2. Assuming a Poisson distribution, we will want to find the probability that a 24 ft? piece of sheet metal has at least 17 defects a. First find the mean number of defects per 24 ft2 of this sheet metal. Give your answer as a fraction with no 3 defects then you would type "3/4" in the answer units (for example, if you find the mean to be 4 24 ft? box) defects Preview 24 ft b. Then find the probability that a 24 ft2 piece ofthis sheet metal has at least 17 defects. Round this answer to 4 places after the decimal point, if necessary P(at least 17 defects)

Explanation / Answer

Answer to question # 1)

Answer to part a)

We have mean = 9 defects per 13 ft^2

We want to find mean per 24 ft^2

.

we got 9 defects in 13 ft^2

thus number of defects in 1 ft^2 = 9/13

Number of defects in 24 ft^2 = (9/13) * 24 = 16.6154 defects per 24 ft^2

Since we need to mention this value in fractional form only it would be :

(9/13 ) * 24 = 216 /13

.

Answer to part b)

Thus we got mean = 16.6154 and we need to find P(X 17)

P(x 17) = 1 - P(x 16)

we need to find cumulative poisson probability for Mean = 216/13 and x = 16

we get: P(x 16) = 0.505

.

Thus probability P(x 17) = 1 - 0.505

P(x 17) = 0.495

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