Suppose x has a distribution with a mean of 40 and a standard deviation of 3. Random samples of size n = 36 are drawn.

(a) Describe thex bar distribution.

x bar has a binomial distribution.

x bar has a Poisson distribution.

x bar has an approximately normal distribution.

x bar has a geometric distribution.

x bar has an unknown 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 tox 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 36 from the x distribution to have a sample mean less than 41? Explain.

Yes, it would be unusual because less 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 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.