Chapter 07: Worked example of Probability of the sample mean CLT, SEM. Worked example 7.5
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You mention two things that are of concern. 1. The population doesn't have to be a bell shaped curve, and 2. The sampling distribution of the mean is always bell shaped. The first statement is true, but if the population isn't normal, then the CLT may not work well enough for n=25. It would depend on how the population is distributed. The second statement is false. The sampling distribution of the mean is always normal *only if* the population is normal.
palui 1 year ago