Historical data for a local steel manufacturing company shows that the average number of defects per standard sheet of steel is 2.In addition,the number of defects per unit is distributed according to Poisson distribution. Determine the standard deviation of the number of defective units for 32 sheets of metal.
A)2
B)32
C)64
D)8

Question

Quizplus · Accepted Answer

The Poisson distribution has only one parameter, which is the mean, and the mean and variance are equal in this case. Therefore, the standard deviation of the number of defects per standard sheet of steel is the square root of the mean:

sqrt(2) ≈ 1.41

The standard deviation of the number of defective units for 32 sheets of metal is simply the standard deviation of the number of defects per sheet multiplied by the square root of the number of sheets:

σ = 1.41 * sqrt(32) ≈ 8

Therefore, the best choice is D, with a standard deviation of 8.

Historical Data for a Local Steel Manufacturing Company Shows That