Normal Distribution

Question

Private nonprofit four-year colleges charge, on average, $26,136 per year in tuition and fees. The standard deviation is $7,482. 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 29,167 per year. ______

c. Find the 67th percentile for this distribution. $ (Round to the nearest dollar.)_______

Answer 1

a. What is the distribution of X? X ~ N($26136,5598331684)

b. Find the probability that a randomly selected Private nonprofit four-year college will cost less than 29,167 per year. 

Let X be the cost. Then using the normal standardization we have

P(X<29,167)=P((X-26,136)/7,482)<(29,167-26,136)/7,482)

=P(Z<0.4051056)

=0.6573

c. Find the 67th percentile for this distribution. $ (Round to the nearest dollar.)_______

I will use the normal standard formula

z=(x-µ)/sd

with the information of 67th percentile we can compute the z value using normal standard tables. z=0.4399132. Plugin this z-value, the mean, and the standard deviatin in the formula we have

0.4399132=(x-26,13)/7,482

No we solve for x:

x=5904.431

then rounding to the nearest dollar x=5904