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A population has a mean of 75 and a standard deviation of 32. Suppose a random...

A population has a mean of 75 and a standard deviation of 32. Suppose a random sample size of 80 will be taken.

1. What are the expected value and the standard deviation of the sample mean x ̅?

2. Describe the probability distribution to x ̅. Draw a graph of this probability distribution of x ̅ with its mean and standard deviation.

3. What is the probability that the sample mean is greater than 85? What is the probability that the sample mean falls between than 65 and 70?

4. What is the probability that the sample mean will be within ± 6 of the population mean?

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