Supposexhas a distribution with a mean of70and a standard deviation of51. Random samples of sizen=36are drawn.

(a) Describe thedistribution. x bar has a normal distribution.

x bar has a geometric distribution.

x bar has a binomial distribution.

x bar has a Poisson distribution.

x bar has an unknown distribution.

x bar has an approximately 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 thezvalue corresponding to=87. (Enter an exact number.) z= (c) FindP(<87). (Enter a number. Round your answer to four decimal places.) P(<87) =P(x bar < 87) (d) Would it be unusual for a random sample of size36from thexdistribution to have a sample mean less than87? Explain. No, it would not be unusual because less than 5% of all such samples have means less than 87.

No, it would not be unusual because more than 5% of all such samples have means less than 87.

Yes, it would be unusual because more than 5% of all such samples have means less than 87.

Yes, it would be unusual because less than 5% of all such samples have means less than 87.