Question

Private nonprofit four-year colleges charge, on average, $26,013 per year in tuition and fees. The standard deviation is $6,728. 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 28,730 per year.

c. Find the 63rd percentile for this distribution. $ (Round to the nearest dollar.)

Answer 1

Part a.

X ~ N (26013,6728 )

Part b .

X = 28,730

Z score :

P( X < 28,730 ) = P( Z < 0.4038 ) = 0.6568           

( We find this using excel command =NORMSDIST(0.4038))

Answer : 0.6568 is the probability that a randomly selected Private nonprofit four-year college will cost less than 28,730 per year

Part c .

Area= 63% = 0.63

Using normal table or excel command =NORMSINV(0.63) use to find Z

Z = 0.3319

Answer : 63rd percentile for this distribution is 28245