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

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

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