Compute P(X) using the binomial probability formula. Then determine whether the normal distribution can be used to estimate this probability. If so, approximate P(2 using the normal distribution and compare the result with the exact probability. n = 52, p = 0.3, and X = 15 ..... For n = 52, p = 0.3, and X = 15, use the binomial probability formula to find P(X). (Round to four decimal places as needed.) Can the normal distribution be used to approximate this probability? O A. Yes, because np(1 - p) 2 10 O B. No, because np(1- p) s 10 OC. No, because np(1 - p) s 10 O D. Yes, because ynp(1 - p) 2 10 Approximate P(X) using the normal distribution. Use a standard normal distribution table. O A. P(X) = (Round to four decimal places as needed.) O B. The normal distribution cannot be used. By how much do the exact and approximated probabilities differ? (Round to four decimal places as needed.) O B. The normal distribution cannot be used.
Compute P(X) using the binomial probability formula. Then determine whether the normal distribution can be used to estimate this probability. If so, approximate P(2 using the normal distribution and compare the result with the exact probability. n = 52, p = 0.3, and X = 15 ..... For n = 52, p = 0.3, and X = 15, use the binomial probability formula to find P(X). (Round to four decimal places as needed.) Can the normal distribution be used to approximate this probability? O A. Yes, because np(1 - p) 2 10 O B. No, because np(1- p) s 10 OC. No, because np(1 - p) s 10 O D. Yes, because ynp(1 - p) 2 10 Approximate P(X) using the normal distribution. Use a standard normal distribution table. O A. P(X) = (Round to four decimal places as needed.) O B. The normal distribution cannot be used. By how much do the exact and approximated probabilities differ? (Round to four decimal places as needed.) O B. The normal distribution cannot be used.
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
![### Binomial and Normal Distribution Approximation
**Problem Statement:**
Compute P(X) using the binomial probability formula. Then determine whether the normal distribution can be used to estimate this probability. If so, approximate P(X) using the normal distribution and compare the result with the exact probability.
Given:
- n = 52
- p = 0.3
- X = 15
**Steps for Solution:**
1. **Binomial Probability Calculation:**
Compute P(X) for n = 52, p = 0.3, and X = 15 using the binomial probability formula.
- Input your answer in the box provided and round to four decimal places as needed.
\[
[\_\_\_\_]
\]
2. **Normal Distribution Approximation Criteria:**
Determine if the normal distribution can be used to approximate this probability by checking the following condition:
\[
np(1-p) \ge 10 \quad \text{or} \quad \sqrt{np(1-p)} \ge 10
\]
Choose one:
- A. Yes, because \(np(1-p) \ge 10\)
- B. No, because \(\sqrt{np(1-p)} \le 10\)
- C. No, because \(np(1-p) \le 10\)
- D. Yes, because \(\sqrt{np(1-p)} \ge 10\)
3. **Approximation Using Normal Distribution:**
If applicable, approximate P(X) using a standard normal distribution table.
- Choose one:
- A. P(X) = \([ \_\_\_\_ ]\) (round to four decimal places as needed)
- B. The normal distribution cannot be used.
4. **Comparison of Exact and Approximated Probabilities:**
Determine how much the exact and approximated probabilities differ.
- Choose one:
- A. \([ \_\_\_\_ ]\) (round to four decimal places as needed)
- B. The normal distribution cannot be used.
Use appropriate formulas and statistical tables to calculate and input values where \([ \_\_\_\_ ]\) is indicated.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdda07105-6c0d-411b-9881-d7cffef7fce9%2F6974ad8d-b9ca-4a7c-94dd-7e86886eb51d%2Fsnxz69g_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Binomial and Normal Distribution Approximation
**Problem Statement:**
Compute P(X) using the binomial probability formula. Then determine whether the normal distribution can be used to estimate this probability. If so, approximate P(X) using the normal distribution and compare the result with the exact probability.
Given:
- n = 52
- p = 0.3
- X = 15
**Steps for Solution:**
1. **Binomial Probability Calculation:**
Compute P(X) for n = 52, p = 0.3, and X = 15 using the binomial probability formula.
- Input your answer in the box provided and round to four decimal places as needed.
\[
[\_\_\_\_]
\]
2. **Normal Distribution Approximation Criteria:**
Determine if the normal distribution can be used to approximate this probability by checking the following condition:
\[
np(1-p) \ge 10 \quad \text{or} \quad \sqrt{np(1-p)} \ge 10
\]
Choose one:
- A. Yes, because \(np(1-p) \ge 10\)
- B. No, because \(\sqrt{np(1-p)} \le 10\)
- C. No, because \(np(1-p) \le 10\)
- D. Yes, because \(\sqrt{np(1-p)} \ge 10\)
3. **Approximation Using Normal Distribution:**
If applicable, approximate P(X) using a standard normal distribution table.
- Choose one:
- A. P(X) = \([ \_\_\_\_ ]\) (round to four decimal places as needed)
- B. The normal distribution cannot be used.
4. **Comparison of Exact and Approximated Probabilities:**
Determine how much the exact and approximated probabilities differ.
- Choose one:
- A. \([ \_\_\_\_ ]\) (round to four decimal places as needed)
- B. The normal distribution cannot be used.
Use appropriate formulas and statistical tables to calculate and input values where \([ \_\_\_\_ ]\) is indicated.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 1 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