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Suppose that we know that scores on a nationally administered statistics examination follow a uniform distribution with a population mean µ = 70 and population standard deviation σ = 20. A random sample of n = 64 is taken. Answer each of the following.
- What is the probability distribution for the sample mean?
- What is the value of the standard deviation of the sample mean?
- What is the probability that the sample mean is below 71?
- What is the probability that the sample mean is above 72?