ompute 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) usir ormal distribution and compare the result with the exact probability. n = 53, p=0.7, and X = 41 or 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.) an the normal distribution be used to approximate this probability? A. Yes, because √np(1-p) ≥10 OB. No, because np(1-p) ≤ 10 OC. No, because √np(1-p) ≤ 10 D. Yes, because np(1-p) 2 10 pproximate P(X) using the normal distribution. Use a standard normal distribution table. A. P(X)= 0.0605 (Round to four decimal places as needed.)
ompute 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) usir ormal distribution and compare the result with the exact probability. n = 53, p=0.7, and X = 41 or 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.) an the normal distribution be used to approximate this probability? A. Yes, because √np(1-p) ≥10 OB. No, because np(1-p) ≤ 10 OC. No, because √np(1-p) ≤ 10 D. Yes, because np(1-p) 2 10 pproximate P(X) using the normal distribution. Use a standard normal distribution table. A. P(X)= 0.0605 (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
Related questions
Question
![### Educational Content on Binomial Probability Computation
**Objective:**
To compute \( P(X) \) using the binomial probability formula, and to determine whether the normal distribution can be used for approximation. If applicable, the result is compared with the exact probability.
**Given Parameters:**
- \( n = 53 \)
- \( p = 0.7 \)
- \( X = 41 \)
**Steps:**
1. **Compute \( P(X) \) using the Binomial Probability Formula:**
\[
P(X) = 0.0632 \quad \text{(Rounded to four decimal places as needed)}
\]
2. **Determine if the Normal Distribution Can Be Used:**
- Criteria for using normal approximation:
- \( \sqrt{np(1-p)} \geq 10 \) or
- \( np(1-p) \geq 10 \)
- 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: Option D is selected.
3. **Approximate \( P(X) \) using the Normal Distribution:**
- Use a standard normal distribution table.
\[
P(X) \approx 0.0605 \quad \text{(Rounded to four decimal places as needed)}
\]
4. **Calculate the Difference between Exact and Approximated Probabilities:**
- By how much do the exact and approximated probabilities differ?
- A. (Round to four decimal places as needed)
- B. The normal distribution cannot be used.
**Note:**
This exercise demonstrates how to use both binomial formulas and normal approximation methods for probability calculation. The closeness of \( 0.0632 \) and \( 0.0605 \) suggests a reasonable approximation under the given conditions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5b37097f-a982-4074-a95e-7bc00cf4b046%2F9515fd0b-4d4b-46a7-bffd-2c1c46a456d7%2Fnkiej5k_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Educational Content on Binomial Probability Computation
**Objective:**
To compute \( P(X) \) using the binomial probability formula, and to determine whether the normal distribution can be used for approximation. If applicable, the result is compared with the exact probability.
**Given Parameters:**
- \( n = 53 \)
- \( p = 0.7 \)
- \( X = 41 \)
**Steps:**
1. **Compute \( P(X) \) using the Binomial Probability Formula:**
\[
P(X) = 0.0632 \quad \text{(Rounded to four decimal places as needed)}
\]
2. **Determine if the Normal Distribution Can Be Used:**
- Criteria for using normal approximation:
- \( \sqrt{np(1-p)} \geq 10 \) or
- \( np(1-p) \geq 10 \)
- 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: Option D is selected.
3. **Approximate \( P(X) \) using the Normal Distribution:**
- Use a standard normal distribution table.
\[
P(X) \approx 0.0605 \quad \text{(Rounded to four decimal places as needed)}
\]
4. **Calculate the Difference between Exact and Approximated Probabilities:**
- By how much do the exact and approximated probabilities differ?
- A. (Round to four decimal places as needed)
- B. The normal distribution cannot be used.
**Note:**
This exercise demonstrates how to use both binomial formulas and normal approximation methods for probability calculation. The closeness of \( 0.0632 \) and \( 0.0605 \) suggests a reasonable approximation under the given conditions.
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