Supposexhas a distribution with a mean of40and a standard deviation of12. Random samples of sizen=64are drawn.(a) Describe thedistribution. has an approximately normal distribution. has an unknown distribution. has a binomial distribution. has a Poisson distribution. has a normal distribution. has a geometric 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=37. (Enter an exact number.) z= (c) FindP(<37). (Enter a number. Round your answer to four decimal places.) P(<37) =P(x bar < 37) (d) Would it be unusual for a random sample of size64from thexdistribution to have a sample mean less than37? Explain. No, it would not be unusual because more than 5% of all such samples have means less than 37.No, it would not be unusual because less than 5% of all such samples have means less than 37. Yes, it would be unusual because more than 5% of all such samples have means less than 37.Yes, it would be unusual because less than 5% of all such samples have means less than 37.