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Basic Computation: Binomial Distribution Consider a binomial experiment with n = 7 trials where the probability of success on a single trial is p = 0.60. (a) Find P(r = 7). (b) Find P(r ≤ 6) by using the complement rule.

Basic Computation: Binomial Distribution Consider a binomial experiment with n = 7 trials where the probability of success on a single trial is p = 0.60. (a) Find P(r = 7). (b) Find P(r ≤ 6) by using the complement rule.

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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Answer number 12. All parts! Show work! Thanks!
### Basic Computations and Interpretations: Binomial Distribution **Problem 12:** **Basic Computation: Binomial Distribution** Consider a binomial experiment with \( n = 7 \) trials where the probability of success on a single trial is \( p = 0.60 \). (a) Find \( P(r = 7) \). (b) Find \( P(r \leq 6) \) by using the complement rule. --- **Problem 13:** **Basic Computation: Binomial Distribution** Consider a binomial experiment with \( n = 6 \) trials where the probability of success on a single trial is \( p = 0.85 \). (a) Find \( P(r \leq 1) \). (b) **Interpretation**: If you conducted the experiment and got fewer than 2 successes, would you be surprised? Why? --- ### Explanation: In Problems 12 and 13, we are dealing with binomial distributions to find probabilities of a certain number of successes in given trials. This involves understanding and applying concepts such as the probability of a single trial, the number of trials, and using the complement rule to find cumulative probabilities. **Key Concepts:** - **Binomial Distribution**: A probability distribution that summarizes the likelihood that a value will take one of two independent values under a given set of parameters or assumptions. **Problem 12:** - **Part (a)** asks us to find the exact probability of achieving 7 successes (all trials resulting in success). - **Part (b)** requires us to use the complement rule, which states that the probability of an event occurring is 1 minus the probability of it not occurring. **Problem 13:** - **Part (a)** requires computing the probability of having 1 or fewer successes. - **Part (b)** asks for an interpretation of the results in a practical context, evaluating whether the outcome would be surprising based on the computed probabilities.
Transcribed Image Text:### Basic Computations and Interpretations: Binomial Distribution **Problem 12:** **Basic Computation: Binomial Distribution** Consider a binomial experiment with \( n = 7 \) trials where the probability of success on a single trial is \( p = 0.60 \). (a) Find \( P(r = 7) \). (b) Find \( P(r \leq 6) \) by using the complement rule. --- **Problem 13:** **Basic Computation: Binomial Distribution** Consider a binomial experiment with \( n = 6 \) trials where the probability of success on a single trial is \( p = 0.85 \). (a) Find \( P(r \leq 1) \). (b) **Interpretation**: If you conducted the experiment and got fewer than 2 successes, would you be surprised? Why? --- ### Explanation: In Problems 12 and 13, we are dealing with binomial distributions to find probabilities of a certain number of successes in given trials. This involves understanding and applying concepts such as the probability of a single trial, the number of trials, and using the complement rule to find cumulative probabilities. **Key Concepts:** - **Binomial Distribution**: A probability distribution that summarizes the likelihood that a value will take one of two independent values under a given set of parameters or assumptions. **Problem 12:** - **Part (a)** asks us to find the exact probability of achieving 7 successes (all trials resulting in success). - **Part (b)** requires us to use the complement rule, which states that the probability of an event occurring is 1 minus the probability of it not occurring. **Problem 13:** - **Part (a)** requires computing the probability of having 1 or fewer successes. - **Part (b)** asks for an interpretation of the results in a practical context, evaluating whether the outcome would be surprising based on the computed probabilities.
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