Question

In: Statistics and Probability

Private nonprofit four-year colleges charge, on average, $26,755 per year in tuition and fees. The standard...

Private nonprofit four-year colleges charge, on average, $26,755 per year in tuition and fees. The standard deviation is $6,752. 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 25,013 per year.

c. Find the 66th percentile for this distribution. $ (Round to the nearest dollar.)

c. Find the 66th percentile for this distribution. $Incorrect (Round to the nearest dollar.) 29540

Please show step by step.

Expert Solution

We are given the following information in the question:

Mean, μ = $26755 per year

Standard Deviation, σ = $6752

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 $25,013 per year.

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

c) 66th percentile for the distribution.

We have to find the value of x such that the probability is 0.66

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

x=31211.32

The 70th percentile for the distribution of college cost is 31211.32

orchestra answered 1 year ago

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