Question

The mean and standard deviation for a process are μ = 85 and σ = 10. For the variable control chart, a sample size of 21 will be used. The standard deviation of the sampling distribution is

2.18

1.84

1.92

2.12

2.25

Answer 1

Answer: The standard deviation of the sampling distribution is 2.18. Thus, option 1 is correct.

Step-by-step explanation:

Given:

Mean=85

Standard deviation = 10

Number of sample size n= 21

Now,

The standard deviation of the sampling distribution= σ/
`√(n)`

=10/
`√(21)` = 2.18

The Sampling Distribution of Standard Deviation estimates the standard deviation of the samples that approximates closely to the population standard deviation, in case the population standard deviation is not easily known. Thus, the sample standard deviation (S) can be used in the place of population standard deviation (σ). Symbolically,σ=S/
`√(n)`

S= standard error of the standard deviation and n =sample size.