The medicaldegree.com reported  the medical doctors’  salary level. The mean salary for the doctor is $250,000 and standard deviation of $100,000. Find the following probabilities assuming that doctor’s salary has a normal distribution.  

A)  What is the probability that the doctor’s salary is higher than $500,000?

B)  What is the probability that the doctor’s salary is less than $100,000?

C)  Suppose we randomly select 36 doctors, what is the probability that the sample mean of doctor’s salary is less than $225,000.

D)  Suppose we don’t have any information about population, and from a sample of 100 doctors, we find the sample mean salary was $255,000 with the standard deviation of $99,500. What is the 95% confidence interval?  

E)  Based on the standard deviation of $100,000 and allow the margin of errors to $20,000, what is your sample size should be at 95% confidence level.