Question

Private nonprofit four-year colleges charge, on average, $27,629 per year in tuition and fees. The standard deviation is $6,833. 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 31,217 per year. ______. round to 4 decimal places

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

Answer 1

Solution :

Given that ,

mean = = 27629

standard deviation = = 6833

a)

X N ( 27629 , 6833)

b)

P(x < 31217) = P((x - ) / < (31217 - 27629) / 6833)

= P(z < 0.53)

= 0.7019

Probability = 0.7019

c)

P(Z < z ) = 66%

P(Z < z ) = 0.66

P(Z < 0.41) = 0.66

z = 0.41

Using z-score formula,

X = z* +

= 0.41 * 6833 + 27629

= 30430.53

= 30431