Question

A carpet manufacturer is inspecting for flaws in the finished product. If there are too many blemishes, the carpet will have to be destroyed. He finds the number of flaws in each square yard and is interested in the average number of flaws per 10 square yards of material. If we assume the standard deviation of the number of flaws per square yard is 0.6, the sample mean, , for the 10 square yards will a standard deviation of

Answer 1

10 square meters will have a standard deviation of 1.897.

Explanation:

Standard deviation for n instances of a variable:

If the standard deviation for one instance of a variable is
`\sigma`, for n instances of the variable, the standard deviation will be of
`s = \sigma√(n)`

The standard deviation of the number of flaws per square yard is 0.6

This means that
`\sigma = 0.6`

For the 10 square yards will a standard deviation of

`n = 10`, so:

`s = \sigma√(n) = 0.6√(10) = 1.897`

10 square meters will have a standard deviation of 1.897.