Your boss tells you that she knows the length of the widgets your company makes is normally distributed with a mean of 25 inches and a population standard deviation of 12 inches. If you take samples of size 9 from finished widgets in the warehouse, in order to check for quality, what will be the mean and standard deviation of the sampling distribution?

Mean of sampling distribution = 25 inches

Standard deviation of sampling distribution = 4 inches

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 25 inches

Standard Deviation, σ = 12 inches

Sample size, n = 9

We are given that the distribution of length of the widgets is a bell shaped distribution that is a normal distribution.

a) Mean of the sampling distribution

The best approximator for the mean of the sampling distribution is the population mean itself.

Thus, we can write:

b) Standard deviation of the sampling distribution

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step-by-step explanation: