Question

Private nonprofit four-year colleges charge, on average, $26,516 per year in tuition and fees. The standard deviation is $7,429. 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 22,272 per year.

c. Find the 62nd percentile for this distribution. $ (Round to the nearest dollar.)

Answer 1

Solution :

Given that ,

mean = = 26516

standard deviation = = 7429

a)

The distribution of X is,

X ~ N( , )

X ~ N(26516 , 7429)

b)

P(x < 22272) = P((x - ) / < (22272 - 26516) / 7429)

= P(z < -0.57)

= 0.2843 Using standard normal table,

Probability = 0.2843

c)

The z - distribution of the 62% is,

P( Z < z ) = 62 %

P( Z < z ) = 0.62

P( Z < 0.31 ) = 0.62

z = 0.31

Using z - score formula,

X = z * +

= 0.31 * 7429 + 26516

= 28818.99

= $28819