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 = 53, p=0.7, and X= 41 For n = 53, p = 0.7, and X=41, use the binomial probability formula to find P(X). 0.0632 (Round to four decimal places as needed.) Can the normal distribution be used to approximate this probability? OA. Yes, because √np(1-p) ≥ 10 оо .. B. No, because np(1-p) ≤ 10 OC. No, because √np(1-p) ≤ 10 OD. Yes, because np(1-p) ≥ 10
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 = 53, p=0.7, and X= 41 For n = 53, p = 0.7, and X=41, use the binomial probability formula to find P(X). 0.0632 (Round to four decimal places as needed.) Can the normal distribution be used to approximate this probability? OA. Yes, because √np(1-p) ≥ 10 оо .. B. No, because np(1-p) ≤ 10 OC. No, because √np(1-p) ≤ 10 OD. Yes, because np(1-p) ≥ 10
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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![**Binomial Probability and Normal Approximation**
**Objective:**
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:**
- \( n = 53 \)
- \( p = 0.7 \)
- \( X = 41 \)
**Calculation:**
For \( n = 53 \), \( p = 0.7 \), and \( X = 41 \), use the binomial probability formula to find \( P(X) \).
\[ P(X) = 0.0632 \]
*Rounded to four decimal places as needed.*
**Question:**
Can the normal distribution be used to approximate this probability?
**Options:**
- **A.** Yes, because \(\sqrt{np(1-p)} \geq 10\)
- **B.** No, because \(np(1-p) \leq 10\)
- **C.** No, because \(\sqrt{np(1-p)} \leq 10\)
- **D.** Yes, because \(np(1-p) \geq 10\)
**Correct Answer: C.** No, because \(\sqrt{np(1-p)} \leq 10\)
**Explanation:**
The normal approximation can generally be used when both \(np\) and \(n(1-p)\) are greater than or equal to 5. The square root condition \(\sqrt{np(1-p)}\) helps assess the variability and accuracy of using a normal approximation. In this case, the condition is not satisfied, indicating that the normal distribution should not be used for approximation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5b37097f-a982-4074-a95e-7bc00cf4b046%2Fef774eb4-4fe2-4603-99a4-a71523235563%2F4bi1fqx_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Binomial Probability and Normal Approximation**
**Objective:**
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:**
- \( n = 53 \)
- \( p = 0.7 \)
- \( X = 41 \)
**Calculation:**
For \( n = 53 \), \( p = 0.7 \), and \( X = 41 \), use the binomial probability formula to find \( P(X) \).
\[ P(X) = 0.0632 \]
*Rounded to four decimal places as needed.*
**Question:**
Can the normal distribution be used to approximate this probability?
**Options:**
- **A.** Yes, because \(\sqrt{np(1-p)} \geq 10\)
- **B.** No, because \(np(1-p) \leq 10\)
- **C.** No, because \(\sqrt{np(1-p)} \leq 10\)
- **D.** Yes, because \(np(1-p) \geq 10\)
**Correct Answer: C.** No, because \(\sqrt{np(1-p)} \leq 10\)
**Explanation:**
The normal approximation can generally be used when both \(np\) and \(n(1-p)\) are greater than or equal to 5. The square root condition \(\sqrt{np(1-p)}\) helps assess the variability and accuracy of using a normal approximation. In this case, the condition is not satisfied, indicating that the normal distribution should not be used for approximation.
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