Suppose x has a distribution with a mean of 50 and a standard deviation of 15. Random samples of size n = 36 are drawn.

(a) Describe the x bar distribution.

x bar has a binomial distribution.

x bar has an unknown distribution.

x bar has a Poisson distribution.

x bar has an approximately normal distribution.

x bar has a geometric distribution.

x bar has a normal 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 = 55. (Enter an exact number.)

z =

(c) Find P(x bar < 55). (Enter a number. Round your answer to four decimal places.)

P(x bar < 55) = P(x bar < 55)

(d) Would it be unusual for a random sample of size 36 from the x distribution to have a sample mean less than 55? Explain.

Yes, it would be unusual because more than 5% of all such samples have means less than 55.

No, it would not be unusual because less than 5% of all such samples have means less than 55.

No, it would not be unusual because more than 5% of all such samples have means less than 55.

Yes, it would be unusual because less than 5% of all such samples have means less than 55.