Concept explainers
Tocalculate:The mean and the standard deviation of the sampling distribution of
Answer to Problem 50E
The required mean and standard deviation are 40.125 millimeters and 0.001 millimeters respectively.
Explanation of Solution
Given information:
Mean = 40.125 millimeters
Standard deviation = 0.002 millimeters
Number of axles = 4
Formula used:
The mean of the sampling distribution of
The standard deviation of a sample distribution of the sample mean
Calculation:
Here, given data can be written as:
Mean,
Population standard deviation,
Sample size, n = 4
It is known that the mean of the sampling distribution of
So, the mean of the sampling distribution of the sample mean
Also, the standard deviation of a sample distribution of the sample mean
Substitute 0.002 for
Hence, the required mean and standard deviation are 40.125 millimeters and 0.001 millimeters respectively.
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The Practice of Statistics for AP - 4th Edition
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