Private nonprofit four-year colleges charge, on average, $26,059 per year in tuition and fees. The standard deviation is $7,129. 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 25,096 per year. c. Find the 61th percentile for this distribution. $ (Round to the nearest dollar.)
Private nonprofit four-year colleges charge, on average, $26,059 per year in tuition and fees. The standard deviation is $7,129. 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 25,096 per year. c. Find the 61th percentile for this distribution. $ (Round to the nearest dollar.)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Transcribed Image Text:**Distribution of Tuition Costs in Private Nonprofit Four-Year Colleges**
Private nonprofit four-year colleges charge, on average, $26,059 per year in tuition and fees. The standard deviation is $7,129. 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?**
\( X \sim N(\text{mean}, \text{standard deviation}^2) \)
b. **Find the probability that a randomly selected Private nonprofit four-year college will cost less than $25,096 per year.**
(Enter the calculated probability in the provided space)
c. **Find the 61st percentile for this distribution.**
\( \$ \text{(Enter the calculated amount rounded to the nearest dollar)} \)
Expert Solution

Step 1
Given
Mean=26059
Standard deviations=7129
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