d) Find the probability of obtaining less than 15 correct questions. e) Would the Normal Approximation produced accurate results? Provide all formulas used. f) Evaluate the probability of obtaining 20 correct questions by using the normal approximation.
d) Find the probability of obtaining less than 15 correct questions. e) Would the Normal Approximation produced accurate results? Provide all formulas used. f) Evaluate the probability of obtaining 20 correct questions by using the normal approximation.
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
Topic Video
Question
Questions a-c are already completed just need d-f completed! thanks :)
![# Educational Exercise on Probability and Statistics
**Exam Context:**
The final exam in a sociology class consists of 100 multiple-choice questions. Each question has 6 possible answers, with only 1 correct option. An unprepared student makes random guesses for all answers.
**Objective:**
Analyze the statistical likelihood of obtaining correct answers using probability.
---
### Exercise Tasks:
**a) Mean and Standard Deviation Calculation**
- **Task:** Find the mean and standard deviation for the number of correct answers. Provide all formulas used.
- **Instructions:**
- Use the binomial probability formula, where the probability of success (\(p\)) is \(1/6\), and the number of trials (\(n\)) is 100.
- Formula for mean (\(\mu\)): \(\mu = n \cdot p\)
- Formula for standard deviation (\(\sigma\)): \(\sigma = \sqrt{n \cdot p \cdot (1-p)}\)
**b) Probability Calculation**
- **Task:** Find the probability of obtaining exactly 10 correct answers.
- **Instructions:**
- Use the binomial probability formula:
\[
P(X=k) = \binom{n}{k} \cdot p^k \cdot (1-p)^{n-k}
\]
where \(k = 10\).
**c) Analyzing Unusual Outcomes**
- **Task:** Determine if it would be unusual for a student to get 10 answers correct. Use a sentence and probability to justify your answer.
- **Instructions:**
- Calculate the probability from part (b).
- Discuss what makes an event "unusual" in probability terms, often addressing whether the probability is below a certain threshold (e.g., 0.05).
### Note:
Use appropriate statistical tools or software for precise computation, rounding all answers to 4 decimal places. Ensure your explanations are clear to support fellow students’ understanding.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbb20c6cf-302d-448e-b0a5-2e60692d1c1d%2Fcb83614e-f52c-41e5-b06d-ceb68a42fc18%2Fll76db9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:# Educational Exercise on Probability and Statistics
**Exam Context:**
The final exam in a sociology class consists of 100 multiple-choice questions. Each question has 6 possible answers, with only 1 correct option. An unprepared student makes random guesses for all answers.
**Objective:**
Analyze the statistical likelihood of obtaining correct answers using probability.
---
### Exercise Tasks:
**a) Mean and Standard Deviation Calculation**
- **Task:** Find the mean and standard deviation for the number of correct answers. Provide all formulas used.
- **Instructions:**
- Use the binomial probability formula, where the probability of success (\(p\)) is \(1/6\), and the number of trials (\(n\)) is 100.
- Formula for mean (\(\mu\)): \(\mu = n \cdot p\)
- Formula for standard deviation (\(\sigma\)): \(\sigma = \sqrt{n \cdot p \cdot (1-p)}\)
**b) Probability Calculation**
- **Task:** Find the probability of obtaining exactly 10 correct answers.
- **Instructions:**
- Use the binomial probability formula:
\[
P(X=k) = \binom{n}{k} \cdot p^k \cdot (1-p)^{n-k}
\]
where \(k = 10\).
**c) Analyzing Unusual Outcomes**
- **Task:** Determine if it would be unusual for a student to get 10 answers correct. Use a sentence and probability to justify your answer.
- **Instructions:**
- Calculate the probability from part (b).
- Discuss what makes an event "unusual" in probability terms, often addressing whether the probability is below a certain threshold (e.g., 0.05).
### Note:
Use appropriate statistical tools or software for precise computation, rounding all answers to 4 decimal places. Ensure your explanations are clear to support fellow students’ understanding.
Transcribed Image Text:d) Find the probability of obtaining less than 15 correct questions.
e) Would the Normal Approximation produce accurate results? Provide all formulas used.
f) Evaluate the probability of obtaining 20 correct questions by using the normal approximation.
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 2 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.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