Suppose x has a distribution with a mean of 90 and a standard deviation of 4. Random samples of size n = 64 are drawn.

(a) Describe the distribution.

has a normal distribution.

has an approximately normal distribution.

has a geometric distribution.

has an unknown distribution.

has a binomial distribution.

has a Poisson 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 = 91. (Enter an exact number.)

z =

(c) Find P( < 91). (Enter a number. Round your answer to four decimal places.)

P( < 91) = P(x bar < 91)

(d) Would it be unusual for a random sample of size 64 from the x distribution to have a sample mean less than 91? Explain.

No, it would not be unusual because more than 5% of all such samples have means less than 91.

Yes, it would be unusual because less than 5% of all such samples have means less than 91.

Yes, it would be unusual because more than 5% of all such samples have means less than 91.

No, it would not be unusual because less than 5% of all such samples have means less than 91.