Suppose a population has the uniform probability distribution given in Figure 6.8. Then the mean…

Suppose a population has the uniform probability distribution given in Figure 6.8. Then the mean and standard deviation of this probability distribution are, respectively, μ = 175 and σ = 14.43. (See Section 5.2 for the formulas for m and σ.) Now suppose a sample of 11 measurements is selected from this population. Describe the sampling distribution of the sample mean  based on the 1,000 sampling experiments discussed in Example 6.2.

Example 6.2

The rolling machine of a steel manufacturer produces sheets of steel of varying thickness. The thickness of a steel sheet follows a uniform distribution with values between 150 and 200 millimeters. Suppose we perform the following experiment over and over again: Randomly sample 11 steel sheets from the production line and record the thickness x of each. Calculate the two sample statistics

M = Median = Sixth sample measurement when the 11 thicknesses are arranged in ascending order

Obtain approximations to the sampling distributions of  and M.