Supposexhas a distribution with a mean of90and a standard deviation of27. Random samples of sizen=36are drawn.

(a) Describe thexdistribution. (select the correct answer) has a normal distribution.

has a binomial distribution.

has an approximately normal distribution.

has a Poisson distribution.

has an unknown distribution. has a geometric distribution.

Compute the mean and standard deviation of the distribution. (For each answer, enter a number.) mean of the distribution = standard deviation of the distribution = (b) Find thezvalue corresponding tox=99. (Enter an exact number.) z= (c) FindP(<99). (Enter a number. Round your answer to four decimal places.) P(<99) =P(x bar < 99) = (d) Would it be unusual for a random sample of size36from thexdistribution to have a sample mean less than99? Explain. (Select the correct answer) No, it would not be unusual because less than 5% of all such samples have means less than 99.

Yes, it would be unusual because more than 5% of all such samples have means less than 99.

No, it would not be unusual because more than 5% of all such samples have means less than 99

.Yes, it would be unusual because less than 5% of all such samples have means less than 99.