Suppose x has a distribution with a mean of 50 and a standard deviation of 36. Random samples of size n = 64 are drawn. (a) Describe the x bar distribution. x bar has a normal distribution. x bar has an approximately normal distribution. x bar has a binomial distribution. x bar has a Poisson distribution. x bar has a geometric distribution. x bar has an unknown distribution. Compute the mean and standard deviation of the distribution. (For each answer, enter a number.) mu sub x bar = mu sub x bar = sigma sub x bar = sigma sub x bar = (b) Find the z value corresponding to x bar = 41. (Enter an exact number.) z = (c) Find P(x bar < 41). (Enter a number. Round your answer to four decimal places.) P(x bar < 41) = P(x bar < 41) (d) Would it be unusual for a random sample of size 64 from the x distribution to have a sample mean less than 41? Explain. Yes, it would be unusual because more than 5% of all such samples have means less than 41. No, it would not be unusual because more than 5% of all such samples have means less than 41. No, it would not be unusual because less than 5% of all such samples have means less than 41. Yes, it would be unusual because less than 5% of all such samples have means less than 41