Private nonprofit four-year colleges charge, on average, $27,293 per year in tuition and fees. The standard deviation is $7,235. Assume the distribution is normal. Let X be the cost for a randomly selected college. Round all answers to two decimal places.

A. X ~ N( , )

B. Find the probability that a randomly selected Private nonprofit four-year college will cost less than $20,000 per year.

C. Find the 70th percentile for this distribution.

a)

b) 0.1567

c)

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = $27,293 per year

Standard Deviation, σ = $7,235

We are given that the distribution of cost of college is a bell shaped distribution that is a normal distribution.

a) Distribution of X

Let X be the cost for a randomly selected college. Then,

b) Probability that a randomly selected Private nonprofit four-year college will cost less than $20,000 per year.

Calculation the value from standard normal z table, we have,  

c) 70th percentile for the distribution.

We have to find the value of x such that the probability is 0.7

Calculation the value from standard normal z table, we have,  

The 70th percentile for the distribution of college cost is $31,084.14

answer: the answer is 40.82

step-by-step explanation: 3.14 x 13(or half of 26) to the power of 2

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