Supposexhas a distribution with a mean of90and a standard deviation of27. Random samples of sizen=36are drawn.(a) Describe thedistribution. has an approximately normal distribution. has an unknown distribution. has a geometric distribution. has a binomial distribution. has a normal 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 thezvalue corresponding to=81. (Enter an exact number.) z= (c) FindP(<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 size36from thexdistribution to have a sample mean less than81? 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.