You may need to use the appropriate appendix table or technology to answer this question. Assume a binomial probability distribution has p = 0.70 and n = 200. (a) What are the mean and standard deviation? (Round your answers to two decimal places.) mean X x standard deviation (b) Is this situation one in which binomial probabilities can be approximated by the normal probability distribution? Explain. No, because np 2 5 and n(1-P) ≥ 5. No, because np < 5 and n(1-p) < 5. O Yes, because np ≥ 5 and n(1-p) ≥ 5. Yes, because n ≥ 30. Yes, because np < 5 and n(1-p) < 5. (c) What is the probability of 120 to 130 successes? Use the normal approximation of the binomial distribution to answer this question. (Round your answer to four decimal places.) X (d) What is the probability of 150 or more successes? Use the normal approximation of the binomial distribution to answer this question. (Round your answer to four decimal places.) x (e) What is the advantage of using the normal probability distribution to approximate the binomial probabilities? The advantage would be that using the normal probability distribution to approximate the binomial probabilities makes the calculations more accurate. The advantage would be that using the normal probability distribution to approximate the binomial probabilities makes the calculations less. accurate. The advantage would be that using the normal probability distribution to approximate the binomial probabilities increases the number of calculations. O The advantage would be that using the the normal probability distribution to approximate the binomial probabilities reduces the number of X m W 2 cricut
You may need to use the appropriate appendix table or technology to answer this question. Assume a binomial probability distribution has p = 0.70 and n = 200. (a) What are the mean and standard deviation? (Round your answers to two decimal places.) mean X x standard deviation (b) Is this situation one in which binomial probabilities can be approximated by the normal probability distribution? Explain. No, because np 2 5 and n(1-P) ≥ 5. No, because np < 5 and n(1-p) < 5. O Yes, because np ≥ 5 and n(1-p) ≥ 5. Yes, because n ≥ 30. Yes, because np < 5 and n(1-p) < 5. (c) What is the probability of 120 to 130 successes? Use the normal approximation of the binomial distribution to answer this question. (Round your answer to four decimal places.) X (d) What is the probability of 150 or more successes? Use the normal approximation of the binomial distribution to answer this question. (Round your answer to four decimal places.) x (e) What is the advantage of using the normal probability distribution to approximate the binomial probabilities? The advantage would be that using the normal probability distribution to approximate the binomial probabilities makes the calculations more accurate. The advantage would be that using the normal probability distribution to approximate the binomial probabilities makes the calculations less. accurate. The advantage would be that using the normal probability distribution to approximate the binomial probabilities increases the number of calculations. O The advantage would be that using the the normal probability distribution to approximate the binomial probabilities reduces the number of X m W 2 cricut
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
![**Title: Calculating Probability Using the Binomial Distribution**
**Question: How would you calculate the probability in part (d) using the binomial distribution? (Use f(x) to denote the binomial probability function.)**
**Options:**
- ( ) P(x ≥ 150) = f(151) + f(152) + f(153) + f(154) + ... + f(200)
- ( ) P(x ≥ 150) = 1 - [f(149) - f(150) - f(151) - f(152) - ... - f(200)]
- (•) P(x ≥ 150) = 1 - [f(0) + f(1) + f(2) + f(3) + ... + f(149)]
- ( ) P(x ≥ 150) = f(0) + f(1) + f(2) + f(3) + ... + f(149) + f(150)
**Explanation of Options:**
1. **Option 1:** Summing the probabilities from 151 to 200.
2. **Option 2:** Incorrect format; appears to subtract frequencies from unity.
3. **Option 3:** Correct; complements the probability from 0 to 149.
4. **Option 4:** Summing from 0 to 150, incorrect method.
**Conclusion:**
To calculate the probability \( P(x \geq 150) \) using the binomial distribution, select the third option. This option correctly uses the complement rule, summing the probabilities from 0 through 149 and subtracting from 1.
**Need Help?**
- Click the "Read It" button for further guidance.
**Notes:**
This instructional content was designed to help students understand the calculation of binomial distribution probabilities, an important concept in statistics.
**Interface Elements:**
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Transcribed Image Text:**Title: Calculating Probability Using the Binomial Distribution**
**Question: How would you calculate the probability in part (d) using the binomial distribution? (Use f(x) to denote the binomial probability function.)**
**Options:**
- ( ) P(x ≥ 150) = f(151) + f(152) + f(153) + f(154) + ... + f(200)
- ( ) P(x ≥ 150) = 1 - [f(149) - f(150) - f(151) - f(152) - ... - f(200)]
- (•) P(x ≥ 150) = 1 - [f(0) + f(1) + f(2) + f(3) + ... + f(149)]
- ( ) P(x ≥ 150) = f(0) + f(1) + f(2) + f(3) + ... + f(149) + f(150)
**Explanation of Options:**
1. **Option 1:** Summing the probabilities from 151 to 200.
2. **Option 2:** Incorrect format; appears to subtract frequencies from unity.
3. **Option 3:** Correct; complements the probability from 0 to 149.
4. **Option 4:** Summing from 0 to 150, incorrect method.
**Conclusion:**
To calculate the probability \( P(x \geq 150) \) using the binomial distribution, select the third option. This option correctly uses the complement rule, summing the probabilities from 0 through 149 and subtracting from 1.
**Need Help?**
- Click the "Read It" button for further guidance.
**Notes:**
This instructional content was designed to help students understand the calculation of binomial distribution probabilities, an important concept in statistics.
**Interface Elements:**
The screenshot includes visible application icons on a MacOS dock, indicating the user is likely working in an educational environment that may involve multitasking across various applications such as web browsers, note-taking apps, and word processors.
For additional assistance or questions, please consult your instructor or refer to the provided resources.
Transcribed Image Text:### Approximating Binomial Probabilities using the Normal Distribution
### Problem Statement:
Assume a binomial probability distribution has \( p = 0.70 \) and \( n = 200 \).
### Questions and Solutions:
#### (a) What are the mean and standard deviation? (Round your answers to two decimal places.)
- **Mean**:
- **Standard Deviation**:
*Note: The answer is not provided in the image.*
#### (b) Is this situation one in which binomial probabilities can be approximated by the normal probability distribution? Explain.
- **Options and Explanation:**
- No, because \( np \ge 5 \) and \( n(1 - p) \ge 5 \).
- No, because \( np < 5 \) and \( n(1 - p) \ge 5 \).
- Yes, because \( np \ge 5 \) and \( n(1 - p) \ge 5 \). **(Correct Answer)**
- Yes, because \( n \ge 30 \).
- Yes, because \( np < 5 \) and \( n(1 - p) \ge 5 \).
#### (c) What is the probability of 120 to 130 successes? Use the normal approximation of the binomial distribution to answer this question. (Round your answer to four decimal places.)
- **Probability**:
- *Note: The answer is not provided in the image.*
#### (d) What is the probability of 150 or more successes? Use the normal approximation of the binomial distribution to answer this question. (Round your answer to four decimal places.)
- **Probability**:
- *Note: The answer is not provided in the image.*
#### (e) What is the advantage of using the normal probability distribution to approximate the binomial probabilities?
- *Options:*
- The advantage would be that using the normal probability distribution to approximate the binomial probabilities makes the calculations more accurate.
- The advantage would be that using the normal probability distribution to approximate the binomial probabilities makes the calculations less accurate.
- The advantage would be that using the normal probability distribution to approximate the binomial probabilities increases the number of calculations.
- **The advantage would be that using the normal probability distribution to approximate the binomial probabilities reduces the number of calculations.** **(Correct Answer)**
#### Explanation:
-
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