Question

Private nonprofit four-year colleges charge, on average, $27,025 per year in tuition and fees. The standard deviation is $7,267. 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 22,077 per year.

c. Find the 64th percentile for this distribution. $ (Round to the nearest dollar.)

Answer 1

a) Distribution of X is X ~ N( 27025 , 7267)

b) P( X < 22077) = P[( X - )/ < (22077-27025)/7267]

P( X < 22077) = P( Z < -0.68)

Using Z table

P( X < 22077) = 0.2483

c)

P64 = +  * Z​​​​​​0.64

Z score corresponding to area to left 0.64

Z​​​​​​0.64 = 0.36

P64 = 27025 + 7267*0.36

P64 = $ 29641