Elephants have the longest pregnancy of all mammals.One species of elephants has a mean gestation period of 525 days and a standard deviation of 32 days.Enough medical study has been done on this variable that we know it follows an approximate normal distribution.

A) Describe the shape and horizontal scaling of the graph of the distribution of lengths of elephant pregnancies.

B) Find the probability that the length of an elephant pregnancy will be greater than 590 days---that is, find P(x > 590).Based upon your result, state whether or not it is unusual for the length of a pregnancy to be greater than 590 days.

C) Suppose all possible samples of size 30, taken from the recorded lengths of pregnancies, are drawn and the mean is found for each resulting sample.Describe the shape and scaling on the graph of the resulting sampling distribution for the sample mean values.Hint: Apply the Central Limit Theorem!

D) Find the probability that the mean number of days of a randomly selected sample of 30 elephant pregnancy lengths is greater than 533 days.Based upon your result, state whether or not it is unusual to randomly select a sample of 30 elephant pregnancy lengths whose mean is greater than 533 days, and explain why you chose "unusual" or "not unusual" as your answer

E) Find the probability that the mean from a sample of 30 elephant pregnancies will have a mean length between 515 and 535 days.