**Title: Understanding Distribution and Percentiles in College Tuition Costs****Introduction:**In this lesson, we will explore the distribution of tuition costs for private nonprofit four-year colleges. Specifically, we will analyze the average cost, the standard deviation, and how to calculate probabilities and percentiles using the normal distribution.**Problem Statement:**Private nonprofit four-year colleges charge, on average, $27,552 per year in tuition and fees. The standard deviation is $7,325. Assume the distribution is normal. Let $ X $ be the cost for a randomly selected college. Round all answers to 4 decimal places where possible.**Tasks:**a. **Determine the Distribution of Tuition Costs:** What is the distribution of $ X $? Express the normal distribution in the form of $ X \sim N(\mu, \sigma) $.b. **Calculate the Probability:** Find the probability that a randomly selected private nonprofit four-year college will cost less than $24,769 per year.c. **Find the 78th Percentile:** Calculate the 78th percentile for this distribution of tuition costs. Round to the nearest dollar.**Conclusion:**Through these exercises, you will gain a practical understanding of how normal distributions are used to model real-world data, like college tuition costs, and how to apply statistical methods to interpret that data.

Given Data Population Mean,μ = 27552 Population Standard Deviation,σ = 7325 X…

Answered: Round all answers to 4 decimal places…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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