b. What is the distribution of I? NO 156000 948.8330 c. For a single randomly selected graduate, find the probability that her salary is between $148,3 $155,155. 0.08963 d. For a simple random sample of 11 graduates, find the probability that the average salary is bet $148,332 and $155,155. e. For part d), is the assumption of normal necessary? O No Yes
b. What is the distribution of I? NO 156000 948.8330 c. For a single randomly selected graduate, find the probability that her salary is between $148,3 $155,155. 0.08963 d. For a simple random sample of 11 graduates, find the probability that the average salary is bet $148,332 and $155,155. e. For part d), is the assumption of normal necessary? O No Yes
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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![**Survey Analysis on MBA Graduates' Salaries**
**Overview:**
Business Weekly conducted a survey of graduates from 30 top MBA programs. Based on the survey, it is assumed that the mean annual salary for graduates 10 years after graduation is $156,000, with a standard deviation of $30,000. A simple random sample of 11 graduates is taken. All answers are rounded to four decimal places.
**Tasks:**
1. **Distribution of \( X \):**
\[
X \sim N \left( 156000, 30000 \right)
\]
2. **Distribution of \( \bar{X} \):**
\[
\bar{X} \sim N \left( 156000, 9488.330 \right)
\]
3. **Probability Calculation for a Single Graduate:**
To find the probability that a single randomly selected graduate's salary is between $148,332 and $155,155:
\[
\boxed{0.08963}
\]
4. **Probability Calculation for the Average Salary of 11 Graduates:**
To find the probability that the average salary of a sample of 11 graduates is between $148,332 and $155,155:
\[
\boxed{\phantom{}
}
\]
5. **Assumption of Normality:**
For part (d), the assumption of normality is necessary. Check whether it is:
\[
\circ \; \text{No} \quad \circ \; \text{Yes}
\]
Explanation:
**Graphs/Diagrams:**
This text does not contain any graphs or diagrams but presents a series of questions regarding statistical distributions and probability calculations for MBA graduates' salaries. The notation \( N(\mu, \sigma) \) represents a normal distribution with mean \(\mu\) and standard deviation \(\sigma\).
The calculations involve standard statistical methods used in analyzing data sets, particularly focusing on the distribution of salaries and the probabilities associated with salary ranges.
**Probabilistic Analysis:**
- The probability for a selected graduate's salary falling within a range is computed using properties of the normal distribution.
- The probability computation for a sample mean requires adjustments in standard deviation, reflecting the sample size via the Central Limit Theorem.
These exercises are crucial in understanding descriptive and inferential statistics applied to real-world scenarios like](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faa28b18f-3e2d-4592-9d09-7b963ee49630%2Fb10199fa-528a-4a7d-9153-de04f017faa1%2F4fx8rx_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Survey Analysis on MBA Graduates' Salaries**
**Overview:**
Business Weekly conducted a survey of graduates from 30 top MBA programs. Based on the survey, it is assumed that the mean annual salary for graduates 10 years after graduation is $156,000, with a standard deviation of $30,000. A simple random sample of 11 graduates is taken. All answers are rounded to four decimal places.
**Tasks:**
1. **Distribution of \( X \):**
\[
X \sim N \left( 156000, 30000 \right)
\]
2. **Distribution of \( \bar{X} \):**
\[
\bar{X} \sim N \left( 156000, 9488.330 \right)
\]
3. **Probability Calculation for a Single Graduate:**
To find the probability that a single randomly selected graduate's salary is between $148,332 and $155,155:
\[
\boxed{0.08963}
\]
4. **Probability Calculation for the Average Salary of 11 Graduates:**
To find the probability that the average salary of a sample of 11 graduates is between $148,332 and $155,155:
\[
\boxed{\phantom{}
}
\]
5. **Assumption of Normality:**
For part (d), the assumption of normality is necessary. Check whether it is:
\[
\circ \; \text{No} \quad \circ \; \text{Yes}
\]
Explanation:
**Graphs/Diagrams:**
This text does not contain any graphs or diagrams but presents a series of questions regarding statistical distributions and probability calculations for MBA graduates' salaries. The notation \( N(\mu, \sigma) \) represents a normal distribution with mean \(\mu\) and standard deviation \(\sigma\).
The calculations involve standard statistical methods used in analyzing data sets, particularly focusing on the distribution of salaries and the probabilities associated with salary ranges.
**Probabilistic Analysis:**
- The probability for a selected graduate's salary falling within a range is computed using properties of the normal distribution.
- The probability computation for a sample mean requires adjustments in standard deviation, reflecting the sample size via the Central Limit Theorem.
These exercises are crucial in understanding descriptive and inferential statistics applied to real-world scenarios like
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