Suppose x has a distribution with a mean of 70 and a standard deviation of 44. Random samples of size n = 64 are drawn. (a)

Describe the distribution.

has an unknown distribution. has a normal distribution. has a geometric distribution. has a Poisson distribution. has an approximately normal distribution. has a binomial 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 = 81. (Enter an exact number.)

z =

(c)

Find P( < 81). (Enter a number. Round your answer to four decimal places.)

P( < 81) = P(x bar < 81)

(d)

Would it be unusual for a random sample of size 64 from the x distribution to have a sample mean less than 81? Explain.

Yes, it would be unusual because more than 5% of all such samples have means less than 81. No, it would not be unusual because less than 5% of all such samples have means less than 81. No, it would not be unusual because more than 5% of all such samples have means less than 81. Yes, it would be unusual because less than 5% of all such samples have means less than 81.