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 $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. a. What is the distribution of X? X - N( b. What is the distribution of ? N 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? Yes No
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 $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. a. What is the distribution of X? X - N( b. What is the distribution of ? N 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? Yes No
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
100%
![**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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faa28b18f-3e2d-4592-9d09-7b963ee49630%2F5b2c5b6f-85fb-45f5-9a22-832a3aa652c0%2F62dsw0q_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**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
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 3 images
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman