2. Let x be a random variable that represents white blood cell count per cubic milliliter of whole blood. Assume that x has a distribution that is approximately normal, with mean 7500 and population standard deviation 1750. A test result of less than 3500 is an indication of leukopenia. This indicates bone marrow depression that may be the result of a viral infection. Suppose a doctor uses the average x for a random sample of four tests. Answer the following questions showing all steps.

a. Determine the mean and the standard deviation of the sampling distribution of x. Is this distribution normal? Explain how you can tell.

b. What is the probability of getting a sample mean less than 3500?