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(a) Find the probability that the number who have encountered fraudulent charges on their credit cards is (a) exactly 73, (b) at least 73, and (c) fewer than 73. (Round to four decimal places as needed.)

(a) Find the probability that the number who have encountered fraudulent charges on their credit cards is (a) exactly 73, (b) at least 73, and (c) fewer than 73. (Round to four decimal places as needed.)

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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I answered the first part now I just need help with a, b, and c.
**Title: Using Normal Distribution to Approximate Binomial Distribution** **Objective:** Determine whether you can use the normal distribution to approximate the binomial distribution. If possible, use the normal distribution to approximate the indicated probabilities and sketch their graphs. Otherwise, explain why and use the binomial distribution to find the indicated probabilities. **Context:** A survey of adults in a region found that 71% have encountered fraudulent charges on their credit cards. You randomly select 100 adults in the region. Complete parts (a) through (d) below. --- **Step 1: Determine if Normal Approximation is Appropriate** Determine whether a normal distribution can be used to approximate the binomial distribution. Choose the correct answer below. - **A.** Yes, because both np ≥ 5 and nq ≥ 5. (Selected) - **B.** No, because nq < 5. - **C.** No, because np < 5. **Explanation:** The rule of thumb for using the normal approximation is that both np and nq should be greater than or equal to 5, where: - \( n = 100 \) (number of trials) - \( p = 0.71 \) (probability of success) - \( q = 1 - p = 0.29 \) (probability of failure) Calculations: - \( np = 100 \times 0.71 = 71 \) - \( nq = 100 \times 0.29 = 29 \) Since both 71 and 29 are greater than 5, the normal approximation can be used. --- **Step 2: Probability Calculations** Find the probability that the number who have encountered fraudulent charges on their credit cards is: - **(a)** Exactly 73 - **(b)** At least 73 - **(c)** Fewer than 73 **Note:** Round to four decimal places as needed. **Instructions:** Use statistical tools or software to compute these probabilities if not using tables manually. --- **Diagram/Graph Explanation:** - A graph would typically show a bell curve representing the normal distribution. The mean would be at the center (around \( np = 71 \)). - Areas under the curve would illustrate the probabilities of the number of adults encountering fraudulent charges (e.g., exactly 73, at least 73, less than 73). This concludes the section on using the normal
Transcribed Image Text:**Title: Using Normal Distribution to Approximate Binomial Distribution** **Objective:** Determine whether you can use the normal distribution to approximate the binomial distribution. If possible, use the normal distribution to approximate the indicated probabilities and sketch their graphs. Otherwise, explain why and use the binomial distribution to find the indicated probabilities. **Context:** A survey of adults in a region found that 71% have encountered fraudulent charges on their credit cards. You randomly select 100 adults in the region. Complete parts (a) through (d) below. --- **Step 1: Determine if Normal Approximation is Appropriate** Determine whether a normal distribution can be used to approximate the binomial distribution. Choose the correct answer below. - **A.** Yes, because both np ≥ 5 and nq ≥ 5. (Selected) - **B.** No, because nq < 5. - **C.** No, because np < 5. **Explanation:** The rule of thumb for using the normal approximation is that both np and nq should be greater than or equal to 5, where: - \( n = 100 \) (number of trials) - \( p = 0.71 \) (probability of success) - \( q = 1 - p = 0.29 \) (probability of failure) Calculations: - \( np = 100 \times 0.71 = 71 \) - \( nq = 100 \times 0.29 = 29 \) Since both 71 and 29 are greater than 5, the normal approximation can be used. --- **Step 2: Probability Calculations** Find the probability that the number who have encountered fraudulent charges on their credit cards is: - **(a)** Exactly 73 - **(b)** At least 73 - **(c)** Fewer than 73 **Note:** Round to four decimal places as needed. **Instructions:** Use statistical tools or software to compute these probabilities if not using tables manually. --- **Diagram/Graph Explanation:** - A graph would typically show a bell curve representing the normal distribution. The mean would be at the center (around \( np = 71 \)). - Areas under the curve would illustrate the probabilities of the number of adults encountering fraudulent charges (e.g., exactly 73, at least 73, less than 73). This concludes the section on using the normal
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