Private nonprofit four-year colleges charge, on average, $27,175 per year in tuition and fees. The standard deviation is $6,811. Assume the distribution is normal. Let X be the cost for a randomly...

Private nonprofit four-year colleges charge, on average, $27,175 per year in tuition and fees. The standard deviation is $6,811. Assume the distribution is normal. Let X be the cost for a randomly selected college. Round all answers to 4 decimal places where possible.
a. What is the distribution of X? X ~ N(,)


b. Find the probability that a randomly selected Private nonprofit four-year college will cost less than 31,771 per year.


c. Find the 78th percentile for this distribution. $ (Round to the nearest dollar.)