Supposexhas a distribution with a mean of80and a standard deviation of20. Random samples of sizen=64are drawn.

(a)Describe thedistribution.

has an approximately normal distribution.

has a binomial distribution.

has a geometric distribution.

has a Poisson distribution.

has a normal distribution.

has an unknown 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 thezvalue corresponding to=75. (Enter an exact number.)

z=

(c)FindP(<75). (Enter a number. Round your answer to four decimal places.)

P(<75) =

P(x bar < 75)

(d)Would it be unusual for a random sample of size64from thexdistribution to have a sample mean less than75? Explain.

No, it would not be unusual because less than 5% of all such samples have means less than 75.

Yes, it would be unusual because less than 5% of all such samples have means less than 75.

Yes, it would be unusual because more than 5% of all such samples have means less than 75.

No, it would not be unusual because more than 5% of all such samples have means less than 75.