**Understanding Salary Distributions for MBA Graduates**Business Weekly conducted a survey of graduates from 30 top MBA programs. Based on the survey, assume the mean annual salary for graduates 10 years after graduation is $152,000. Assume the standard deviation is $45,000. Suppose you take a simple random sample of 48 graduates. Round all answers to four decimal places if necessary.**Questions and Answers:**a. **What is the distribution of $ X $?** \[ X \sim N(152,000, 45000) \]b. **What is the distribution of $ \overline{X} $?** \[ \overline{X} \sim N(152,000, \frac{45000}{\sqrt{48}}) \]c. **For a single randomly selected graduate, find the probability that her salary is between $142,257 and $147,705.**d. **For a simple random sample of 48 graduates, find the probability that the average salary is between $142,257 and $147,705.**e. **For part d), is the assumption of normal necessary?** \[ \text{Yes} \]In these questions:1. $ X $ represents the salary of a single MBA graduate.2. $ \overline{X} $ represents the average salary of a sample of 48 MBA graduates.3. $ N(\mu, \sigma) $ represents a normal distribution with mean $ \mu $ and standard deviation $ \sigma $.**Explanation of Formulas:**1. **Distribution of $ X $**: - $ X $ follows a normal distribution $ N $ with a mean $ \mu = \$152,000 $ and a standard deviation $ \sigma = \$45,000 $.2. **Distribution of $ \overline{X} $**: - The distribution of the sample mean $ \overline{X} $ also follows a normal distribution, but with a standard deviation adjusted by the square root of the sample size $ n = 48 $.3. **Probability Calculations**: - The probabilities require using the properties of the normal distribution, typically by converting to the standard normal distribution (z-scores).4. **Assumption of Normality**: - The assumption of normality is

Given: Mean = $152000 Standard deviation = $12000 Sample size = 45

Answered: Business Weekly conducted a survey of…

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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