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1. A population with a mean of 1,250 and a standard deviation of 400 is known to be highly skewed to the right. If a random sample of 64 items is selected from the population, what is the probability that the sample mean will be less than 1,325?

2. Suppose that a population is known to be normally distributed with m = 2,000 and s = 230. If a random sample of size n = 8 is selected, calculate the probability that the sample mean will exceed 2,100.

3. A normally distributed population has a mean of 500 and a standard deviation of 60.

a. Determine the probability that a random sample of size 16 selected from this population will have a sample mean less than 475.

b. Determine the probability that a random sample of size 25 selected from the population will have a sample mean greater than or equal to 515.

4. If a population is known to be normally distributed with m = 250 and s = 40, what will be the characteristics of the sampling distribution for x based on a random sample of size 25 selected from the population?

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