Statistics from Cornell's Northeast Regional Climate Center indicate that Ithaca, NY, gets an average of 35.4" of rain each year with a standard deviation of 4.2". Assume the data is normally distributed.
a. What is the probability that Ithaca will get more than 40" of rain?
b. What is the rainfall amount below which the driest 20% of the years in Ithaca lies?
c. A Cornell University student is in Ithaca for 4 years. If we look at the sampling distribution for those four years, what is the mean and standard deviation of those four years.
d. What is the probability that the average rainfall for those four years is less than 30"
e. What is the probability that the average rainfall for those four years is between 30" and 38.7".