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Business Weekly conducted a survey of graduates from 30 top MBA programs. On the basis of the survey, assume the mean annual salary for graduates 10 years after graduation is $181,000. Assume the standard deviation is $32,000. Suppose you take a simple random sample of 39 graduates. Round all answers to four decimal places if necessary. a. What is the distribution of X? X - N( b. What is the distribution of a? x - N( c. For a single randomly selected graduate, find the probability that her salary is between $180,714 and $188,276. d. For a simple random sample of 39 graduates, find the probability that the average salary is between $180,714 and $188,276. e. For part d), is the assumption of normal necessary? O No Yes

Business Weekly conducted a survey of graduates from 30 top MBA programs. On the basis of the survey, assume the mean annual salary for graduates 10 years after graduation is $181,000. Assume the standard deviation is $32,000. Suppose you take a simple random sample of 39 graduates. Round all answers to four decimal places if necessary. a. What is the distribution of X? X - N( b. What is the distribution of a? x - N( c. For a single randomly selected graduate, find the probability that her salary is between $180,714 and $188,276. d. For a simple random sample of 39 graduates, find the probability that the average salary is between $180,714 and $188,276. e. For part d), is the assumption of normal necessary? O No Yes

MATLAB: An Introduction with Applications
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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**Educational Content: Statistical Analysis of MBA Graduate Salaries** **Overview:** Business Weekly conducted a survey of graduates from 30 top MBA programs. Based on the survey, the mean annual salary for graduates 10 years after graduation is $181,000, with a standard deviation of $32,000. Suppose you take a simple random sample of 39 graduates. Round all answers to four decimal places if necessary. --- **Questions and Explanations:** a. **Distribution of X:** - Determine the distribution of the salary \( X \). - Answer format: \( X \sim N(\text{{mean}}, \text{{standard deviation}}) \). b. **Distribution of \(\bar{x}\):** - Determine the distribution of the sample mean \(\bar{x}\). - Answer format: \(\bar{x} \sim N(\text{{mean}}, \text{{standard error}})\). c. **Probability for a Single Graduate:** - Calculate the probability that a randomly selected graduate has a salary between $180,714 and $188,276. - Answer should be calculated and entered in the given box. d. **Probability for Sample Mean:** - For a simple random sample of 39 graduates, calculate the probability that the average salary is between $180,714 and $188,276. - Answer should be calculated and entered in the provided box. e. **Assumption of Normality:** - For part d), determine whether the assumption of normality is necessary. - Answer by selecting either "No" or "Yes". **Instructions for Students:** - Use the properties of normal distribution and standard deviation to solve these questions. - Consider the sample size when determining standard error. - Use a calculator or statistical software for accurate probability results. - Think critically about the necessity of normality for sample means based on the Central Limit Theorem. **Support:** - For questions or further assistance, click on "Message instructor". --- **Submission:** - Once completed, ensure all answers are filled in the answer boxes provided. - Click "Submit Question" to finalize your responses.
Transcribed Image Text:**Educational Content: Statistical Analysis of MBA Graduate Salaries** **Overview:** Business Weekly conducted a survey of graduates from 30 top MBA programs. Based on the survey, the mean annual salary for graduates 10 years after graduation is $181,000, with a standard deviation of $32,000. Suppose you take a simple random sample of 39 graduates. Round all answers to four decimal places if necessary. --- **Questions and Explanations:** a. **Distribution of X:** - Determine the distribution of the salary \( X \). - Answer format: \( X \sim N(\text{{mean}}, \text{{standard deviation}}) \). b. **Distribution of \(\bar{x}\):** - Determine the distribution of the sample mean \(\bar{x}\). - Answer format: \(\bar{x} \sim N(\text{{mean}}, \text{{standard error}})\). c. **Probability for a Single Graduate:** - Calculate the probability that a randomly selected graduate has a salary between $180,714 and $188,276. - Answer should be calculated and entered in the given box. d. **Probability for Sample Mean:** - For a simple random sample of 39 graduates, calculate the probability that the average salary is between $180,714 and $188,276. - Answer should be calculated and entered in the provided box. e. **Assumption of Normality:** - For part d), determine whether the assumption of normality is necessary. - Answer by selecting either "No" or "Yes". **Instructions for Students:** - Use the properties of normal distribution and standard deviation to solve these questions. - Consider the sample size when determining standard error. - Use a calculator or statistical software for accurate probability results. - Think critically about the necessity of normality for sample means based on the Central Limit Theorem. **Support:** - For questions or further assistance, click on "Message instructor". --- **Submission:** - Once completed, ensure all answers are filled in the answer boxes provided. - Click "Submit Question" to finalize your responses.
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