Private nonprofit four-year colleges charge, on average, $27,914 per year in tuition and fees. The standard deviation is $6,717. 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 26,865 per year.c. Find the 60th percentile for this distribution. $ (Round to the nearest dollar.)

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Asked Nov 15, 2019
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Private nonprofit four-year colleges charge, on average, $27,914 per year in tuition and fees. The standard deviation is $6,717. 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 26,865 per year.

c. Find the 60th percentile for this distribution. $ (Round to the nearest dollar.)

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Expert Answer

Step 1

From the given information, mean (μ) = $27,914 and standard deviation (σ) = $6,717.

(a)

Given data normally distributed with mean $27,914 and standard deviation $6,717.

Therefore, distribution of ‘X’ is N~ (μ, σ)

                                                                  ∴ N~ ($27,914, $6,717)

Step 2

(b)

Let ‘X’ be a normal distribution random variable.

Now,

Probability that a randomly selected private nonprofit four year college will cost less than $26,865 per year is,

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26,865-27,914 X- P(X<26,865) P 6,717 -P(Z<-0.1561709096) From the standard normal table P(X<26,865) 0.43644 P(X<26,865) 0.4364 for 4 decimal places

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Step 3

Therefore, Probability that a randomly selected private nonprofit fou...

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