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Part 4 of 4 (d) Would it be unusual if all of them were over the age of 65? Use a cutoff of 0.05. It (Choose one) bé unusual if all of them were over the age of 65. X

Part 4 of 4 (d) Would it be unusual if all of them were over the age of 65? Use a cutoff of 0.05. It (Choose one) bé unusual if all of them were over the age of 65. X

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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I just need help with part D, Please! And an explanation of how to figure it out

**Coronary Bypass Surgery Probability Analysis** **Background Context:** A healthcare agency reports that 80% of people who had coronary bypass surgery in 2008 were over the age of 65. Let's analyze some probabilities based on this information using binomial probability distribution. **Part 1 of 4** **(a) What is the probability that exactly 10 of them are over the age of 65?** - Given 15 coronary bypass patients are sampled. - Calculate the probability that exactly 10 out of these 15 are over the age of 65. - **Answer: 0.2077** (rounded to four decimal places) **Part 2 of 4** **(b) What is the probability that more than 11 are over the age of 65?** - Given 15 coronary bypass patients are sampled. - Calculate the probability that more than 11 out of these 15 are over the age of 65. - **Answer: 0.4796** (rounded to four decimal places) In summary, the provided answers are calculated using binomial distribution where: - The trials (n) = 15 - The probability of success (p, patient over 65 years) = 0.80 *Note*: If using a scientific calculator or software, you would use binomial probability functions to derive these values. **Explanation of Process:** To solve these problems, one typically uses the binomial probability formula or cumulative binomial probability tables/formulas: \[ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \] Where: - \( n \) = number of trials - \( k \) = number of successes - \( p \) = probability of success on an individual trial - \(\binom{n}{k} \) = combination of \( n \) items taken \( k \) at a time For part (b), cumulative probability or complementary probability methods might be used given the ‘more than’ condition.
Transcribed Image Text:**Coronary Bypass Surgery Probability Analysis** **Background Context:** A healthcare agency reports that 80% of people who had coronary bypass surgery in 2008 were over the age of 65. Let's analyze some probabilities based on this information using binomial probability distribution. **Part 1 of 4** **(a) What is the probability that exactly 10 of them are over the age of 65?** - Given 15 coronary bypass patients are sampled. - Calculate the probability that exactly 10 out of these 15 are over the age of 65. - **Answer: 0.2077** (rounded to four decimal places) **Part 2 of 4** **(b) What is the probability that more than 11 are over the age of 65?** - Given 15 coronary bypass patients are sampled. - Calculate the probability that more than 11 out of these 15 are over the age of 65. - **Answer: 0.4796** (rounded to four decimal places) In summary, the provided answers are calculated using binomial distribution where: - The trials (n) = 15 - The probability of success (p, patient over 65 years) = 0.80 *Note*: If using a scientific calculator or software, you would use binomial probability functions to derive these values. **Explanation of Process:** To solve these problems, one typically uses the binomial probability formula or cumulative binomial probability tables/formulas: \[ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \] Where: - \( n \) = number of trials - \( k \) = number of successes - \( p \) = probability of success on an individual trial - \(\binom{n}{k} \) = combination of \( n \) items taken \( k \) at a time For part (b), cumulative probability or complementary probability methods might be used given the ‘more than’ condition.
### Educational Website Content --- **Probability and Statistics: Age Distribution Analysis** **Question:** (c) What is the probability that fewer than 9 are over the age of 65? Round your answer to four decimal places. **Answer:** The probability that fewer than 9 are over the age of 65 is **0.0015**. --- **Alternate Answer:** **The probability that more than 11 are over the age of 65 is 0.0036. The probability that more than 11 are over the age of 65?** **a)** **0.0036** --- **Part 3 of 4** --- **Question:** (d) Would it be unusual if all of them were over the age of 65? Use a cutoff of 0.05. **Answer:** It would **[choose one]** be unusual if all of them were over the age of 65. --- **Navigation:** - Skip Part (Button) - Check (Button) - Save For Later (Button) - Submit (Button) - Terms of Use | Privacy © 2023 McGraw Hill LLC. All Rights Reserved. --- In the diagram above, there are multiple parts with questions focused on calculating probabilities and making inferences based on given statistical data. Each part asks you to compute a probability or make a judgment based on provided figures. In Part (c), you are asked to calculate the probability that fewer than 9 individuals out of a sample group are over the age of 65, which is answered as 0.0015. In Part (d), you need to determine if it would be unusual for all individuals in the sample to be over 65, with a decision-making threshold of 0.05. There's also an alternate answer section providing probabilities for a different scenario related to the age distribution. Make sure to round answers to four decimal places for accuracy and use suitable cutoff levels to determine the unusualness of events as described in part (d). For further questions or clarifications, students are encouraged to utilize the check button for immediate feedback.
Transcribed Image Text:### Educational Website Content --- **Probability and Statistics: Age Distribution Analysis** **Question:** (c) What is the probability that fewer than 9 are over the age of 65? Round your answer to four decimal places. **Answer:** The probability that fewer than 9 are over the age of 65 is **0.0015**. --- **Alternate Answer:** **The probability that more than 11 are over the age of 65 is 0.0036. The probability that more than 11 are over the age of 65?** **a)** **0.0036** --- **Part 3 of 4** --- **Question:** (d) Would it be unusual if all of them were over the age of 65? Use a cutoff of 0.05. **Answer:** It would **[choose one]** be unusual if all of them were over the age of 65. --- **Navigation:** - Skip Part (Button) - Check (Button) - Save For Later (Button) - Submit (Button) - Terms of Use | Privacy © 2023 McGraw Hill LLC. All Rights Reserved. --- In the diagram above, there are multiple parts with questions focused on calculating probabilities and making inferences based on given statistical data. Each part asks you to compute a probability or make a judgment based on provided figures. In Part (c), you are asked to calculate the probability that fewer than 9 individuals out of a sample group are over the age of 65, which is answered as 0.0015. In Part (d), you need to determine if it would be unusual for all individuals in the sample to be over 65, with a decision-making threshold of 0.05. There's also an alternate answer section providing probabilities for a different scenario related to the age distribution. Make sure to round answers to four decimal places for accuracy and use suitable cutoff levels to determine the unusualness of events as described in part (d). For further questions or clarifications, students are encouraged to utilize the check button for immediate feedback.
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