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Determine whether you can use the normal distribution to approximate the binomial distribution. If you can, use the normal distribution to approximate the indicated probabilities and sketch their graphs. If you cannot, explain why and use the binomial distribution to find the indicated probabilities. A survey of adults in a region found that 72% have encountered fraudulent charges on their credit cards. You randomly select 100 adults in the region. Complete parts (a) through (d) below. ..... Determine whether a normal distribution can be used to approximate the binomial distribution. Choose the correct answer below. O A. No, because nq <5. O B. No, because np <5. C. Yes, because both np25 and ng 25. (a) Find the probability that the number who have encountered fraudulent charges on their credit cards is (a) exactly 75, (b) at least 75, and (c) fewer than 75. (Round to four decimal places as needed.) or

Determine whether you can use the normal distribution to approximate the binomial distribution. If you can, use the normal distribution to approximate the indicated probabilities and sketch their graphs. If you cannot, explain why and use the binomial distribution to find the indicated probabilities. A survey of adults in a region found that 72% have encountered fraudulent charges on their credit cards. You randomly select 100 adults in the region. Complete parts (a) through (d) below. ..... Determine whether a normal distribution can be used to approximate the binomial distribution. Choose the correct answer below. O A. No, because nq <5. O B. No, because np <5. C. Yes, because both np25 and ng 25. (a) Find the probability that the number who have encountered fraudulent charges on their credit cards is (a) exactly 75, (b) at least 75, and (c) fewer than 75. (Round to four decimal places as needed.) or

MATLAB: An Introduction with Applications
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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Help please with section (a).it has 3 parts
**Title: Approximating the Binomial Distribution with the Normal Distribution** **Introduction:** The question at hand involves determining whether a normal distribution can be used to approximate a binomial distribution in a given scenario. When certain conditions are met, the normal distribution serves as a useful approximation tool for calculating probabilities in a binomial distribution. **Scenario:** A survey indicates that 72% of adults in a region have encountered fraudulent charges on their credit cards. A random sample of 100 adults from this region is considered to explore further probabilities. **Task:** - Determine if a normal distribution can approximate the binomial distribution. - Calculate the probabilities for the following cases: - Exactly 75 adults encountered fraudulent charges. - At least 75 adults encountered fraudulent charges. - Fewer than 75 adults encountered fraudulent charges. **Conditions for Normal Approximation:** To use the normal distribution as an approximation: - \( np \geq 5 \) and \( nq \geq 5 \), where \( n \) is the sample size, \( p \) is the probability of success, and \( q = 1-p \). **Solution:** Checking the conditions for approximation: - \( n = 100 \), \( p = 0.72 \), \( q = 0.28 \) - Calculate \( np = 100 \times 0.72 = 72 \) - Calculate \( nq = 100 \times 0.28 = 28 \) - Both \( np \) and \( nq \) are greater than 5, making condition **C** applicable: "Yes, because both \( np \geq 5 \) and \( nq \geq 5 \)". **Probability Calculations:** (a) Determine the probability for the number of adults who encountered fraudulent charges: - (a) Exactly 75 - (b) At least 75 - (c) Fewer than 75 Note: Specific probabilities require further calculations using z-scores and normal distribution tables or software. **Conclusion:** Using the normal distribution to approximate binomial probabilities simplifies calculations under these conditions. This approach is particularly useful for large sample sizes, like in this scenario with 100 participants.
Transcribed Image Text:**Title: Approximating the Binomial Distribution with the Normal Distribution** **Introduction:** The question at hand involves determining whether a normal distribution can be used to approximate a binomial distribution in a given scenario. When certain conditions are met, the normal distribution serves as a useful approximation tool for calculating probabilities in a binomial distribution. **Scenario:** A survey indicates that 72% of adults in a region have encountered fraudulent charges on their credit cards. A random sample of 100 adults from this region is considered to explore further probabilities. **Task:** - Determine if a normal distribution can approximate the binomial distribution. - Calculate the probabilities for the following cases: - Exactly 75 adults encountered fraudulent charges. - At least 75 adults encountered fraudulent charges. - Fewer than 75 adults encountered fraudulent charges. **Conditions for Normal Approximation:** To use the normal distribution as an approximation: - \( np \geq 5 \) and \( nq \geq 5 \), where \( n \) is the sample size, \( p \) is the probability of success, and \( q = 1-p \). **Solution:** Checking the conditions for approximation: - \( n = 100 \), \( p = 0.72 \), \( q = 0.28 \) - Calculate \( np = 100 \times 0.72 = 72 \) - Calculate \( nq = 100 \times 0.28 = 28 \) - Both \( np \) and \( nq \) are greater than 5, making condition **C** applicable: "Yes, because both \( np \geq 5 \) and \( nq \geq 5 \)". **Probability Calculations:** (a) Determine the probability for the number of adults who encountered fraudulent charges: - (a) Exactly 75 - (b) At least 75 - (c) Fewer than 75 Note: Specific probabilities require further calculations using z-scores and normal distribution tables or software. **Conclusion:** Using the normal distribution to approximate binomial probabilities simplifies calculations under these conditions. This approach is particularly useful for large sample sizes, like in this scenario with 100 participants.
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