Suppose x has a distribution with a mean of 80 and a standard deviation of 36. Random samples of size n = 64 are drawn.

(a)

Describe the distribution.

has a geometric distribution.

has a Poisson distribution.

has a binomial distribution.

has an unknown distribution.

has an approximately normal distribution. has a normal distribution.

Compute the mean and standard deviation of the distribution. (For each answer, enter a number.) = mu sub x bar = = sigma sub x bar =

(b)

Find the z value corresponding to = 89. (Enter an exact number.) z =

(c)

Find P( < 89). (Enter a number. Round your answer to four decimal places.) P( < 89) = P(x bar < 89)

(d)

Would it be unusual for a random sample of size 64 from the x distribution to have a sample mean less than 89? Explain.

No, it would not be unusual because less than 5% of all such samples have means less than 89.

Yes, it would be unusual because more than 5% of all such samples have means less than 89.

No, it would not be unusual because more than 5% of all such samples have means less than 89.

Yes, it would be unusual because less than 5% of all such samples have means less than 89.