Private nonprofit four-year colleges charge, on average, $26,876 per year in tuition and fees. The standard deviation is $6,777. 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 25,077 per year. c. Find the 73rd percentile for this distribution. $ (Round to the nearest dollar.)

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Asked Nov 16, 2019
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Private nonprofit four-year colleges charge, on average, $26,876 per year in tuition and fees. The standard deviation is $6,777. 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 25,077 per year. 

c. Find the 73rd percentile for this distribution. $ (Round to the nearest dollar.)

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Expert Answer

Step 1

Given:

X be the cost for a randomly selected college.

Mean = μ = 26876

Standard deviation = σ = 6777

So, variance = σ2= 67772=45927729

Step 2

The distribution of x is as follows:

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X N($26,876,$45,927, 729)

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Step 3

b)To find the probability that a randomly selected Private nonprofit four-y...

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Using z-score, X-u25077-26876 Z = 6777 Z=-0.2655

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