Question

Private nonprofit four-year colleges charge, on average, $26,582 per year in tuition and fees. The standard deviation is $6,549. 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(Correct,Correct)

b. Find the probability that a randomly selected Private nonprofit four-year college will cost less than 27,140 per year. Incorrect

c. Find the 66th percentile for this distribution. $ (Round to the nearest dollar.)

Answer 1

Given that, mean (μ) = $26582 and

standard deviation = $6549

a) X ~ N(26582, 6549)

b) We want to find, P(X < 27140)

Therefore, required probability is 0.5359

b) We want to find, the value of x such that, P(X < x) = 0.66

Therefore, the 66th percentile for this distribution is $29267

Note : if we used z-score = 0.41246 instead of 0.41 then we will get, 66th percentile is $29283

Using Excel we get, z-score is,

Excel Command : NORMSINV (0.66) = 0.41246