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. n= 44, p= 0.5, and X = 27 For n = 44, p= 0.5, and X = 27, use the binomial probability formula to find P(X). (Round to four decimal places as needed.)
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. n= 44, p= 0.5, and X = 27 For n = 44, p= 0.5, and X = 27, use the binomial probability formula to find P(X). (Round to four decimal places as needed.)
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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![**Title:** Computing Probability Using the Binomial Formula
**Introduction:**
This exercise focuses on calculating the probability P(X) using the binomial probability formula. It also explores whether the normal distribution can estimate this probability. If applicable, it involves approximating P(X) with the normal distribution and comparing the result to the exact probability.
**Given:**
- Number of trials (n) = 44
- Probability of success (p) = 0.5
- Number of specific successes (X) = 27
**Instructions:**
1. **Step 1:** Compute P(X) using the binomial probability formula.
- For \( n = 44 \), \( p = 0.5 \), and \( X = 27 \), use the formula:
\[
P(X) = \binom{n}{X} p^X (1-p)^{n-X}
\]
- Calculate the binomial coefficient \(\binom{n}{X}\) and the probabilities.
2. **Step 2:** Determine if the normal distribution can estimate P(X).
- Utilize the criteria for normal approximation.
- If valid, proceed with normal approximation methods.
3. **Step 3:** Approximate P(X) using the normal distribution:
- Use the normal approximation method if applicable.
- Compare the approximate result with the exact calculation.
4. **Conclude:**
- Record and interpret the findings.
- Discuss the accuracy and reliability of the normal approximation in this context.
**Note:**
- Ensure all calculations are rounded to four decimal places as needed.
This structured approach ensures comprehensive understanding and application of probability concepts in scenarios where both exact and approximate methods can provide insights.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fac9c6941-fcbd-4d0f-a0fa-57d2e8e41463%2Fd76c7caf-2585-4383-974b-3462ea79929c%2Ffns42t_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title:** Computing Probability Using the Binomial Formula
**Introduction:**
This exercise focuses on calculating the probability P(X) using the binomial probability formula. It also explores whether the normal distribution can estimate this probability. If applicable, it involves approximating P(X) with the normal distribution and comparing the result to the exact probability.
**Given:**
- Number of trials (n) = 44
- Probability of success (p) = 0.5
- Number of specific successes (X) = 27
**Instructions:**
1. **Step 1:** Compute P(X) using the binomial probability formula.
- For \( n = 44 \), \( p = 0.5 \), and \( X = 27 \), use the formula:
\[
P(X) = \binom{n}{X} p^X (1-p)^{n-X}
\]
- Calculate the binomial coefficient \(\binom{n}{X}\) and the probabilities.
2. **Step 2:** Determine if the normal distribution can estimate P(X).
- Utilize the criteria for normal approximation.
- If valid, proceed with normal approximation methods.
3. **Step 3:** Approximate P(X) using the normal distribution:
- Use the normal approximation method if applicable.
- Compare the approximate result with the exact calculation.
4. **Conclude:**
- Record and interpret the findings.
- Discuss the accuracy and reliability of the normal approximation in this context.
**Note:**
- Ensure all calculations are rounded to four decimal places as needed.
This structured approach ensures comprehensive understanding and application of probability concepts in scenarios where both exact and approximate methods can provide insights.
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