Historical data for a local steel manufacturing company show 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 a Poisson distribution.Determine the standard deviation of the number of defects for 32 sheets of metal.
A)2
B)32
C)64
D)8

Question

Quizplus · Accepted Answer

Since the number of defects per unit of steel follows a Poisson distribution, the variance is equal to the mean. Therefore, the variance for one sheet of steel is also 2 defects.

To find the variance for 32 sheets of steel, we can use the fact that the variance of a sum of independent random variables is equal to the sum of the variances. In other words,

Variance of 32 sheets = 32 x Variance of 1 sheet = 32 x 2 = 64

Finally, taking the square root of the variance gives us the standard deviation, which is sqrt(64) = 8.

So, the best choice is D) 8.

Historical Data for a Local Steel Manufacturing Company Show That