Compute the probability of X successes, using the binomial distribution table. Part 1 of 4 (a) n=5, p=0.5, X=4 P(X)=D Part 2 of 4 (b) n=9,p=0.8, X=6 P(X)=D Part 3 of 4 (c) n=12, p=0.3, X=10 P(X)=D !! Part 4 of 4 Continue
Compute the probability of X successes, using the binomial distribution table. Part 1 of 4 (a) n=5, p=0.5, X=4 P(X)=D Part 2 of 4 (b) n=9,p=0.8, X=6 P(X)=D Part 3 of 4 (c) n=12, p=0.3, X=10 P(X)=D !! Part 4 of 4 Continue
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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![## Binomial Probability Exercises
Compute the probability of \( X \) successes, using the binomial distribution table.
### Part 1 of 4
**(a)** \( n = 5, p = 0.5, X = 4 \)
\[ P(X) = \]
Input box with "X" (presumably to clear the input) and a circular arrow icon (likely for resetting or re-calculating).
### Part 2 of 4
**(b)** \( n = 9, p = 0.8, X = 6 \)
\[ P(X) = \]
Input box with "X" and a circular arrow icon.
### Part 3 of 4
**(c)** \( n = 12, p = 0.3, X = 10 \)
\[ P(X) = \]
Input box with "X" and a circular arrow icon.
### Part 4 of 4
("Continue" button at the bottom for progressing to the next part of the exercise.)
This exercise involves calculating the probability of a certain number of successes in a fixed number of trials using the binomial probability formula:
\[
P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}
\]
Where:
- \(\binom{n}{k}\) is the binomial coefficient,
- \(p\) is the probability of success on an individual trial,
- \(n\) is the number of trials,
- \(k\) is the number of successful trials you want to find the probability for.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F01318097-18d7-413e-815c-4ee69f0eee7a%2F6200f343-5376-49af-a188-7c241c89c0f4%2Femsvrd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Binomial Probability Exercises
Compute the probability of \( X \) successes, using the binomial distribution table.
### Part 1 of 4
**(a)** \( n = 5, p = 0.5, X = 4 \)
\[ P(X) = \]
Input box with "X" (presumably to clear the input) and a circular arrow icon (likely for resetting or re-calculating).
### Part 2 of 4
**(b)** \( n = 9, p = 0.8, X = 6 \)
\[ P(X) = \]
Input box with "X" and a circular arrow icon.
### Part 3 of 4
**(c)** \( n = 12, p = 0.3, X = 10 \)
\[ P(X) = \]
Input box with "X" and a circular arrow icon.
### Part 4 of 4
("Continue" button at the bottom for progressing to the next part of the exercise.)
This exercise involves calculating the probability of a certain number of successes in a fixed number of trials using the binomial probability formula:
\[
P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}
\]
Where:
- \(\binom{n}{k}\) is the binomial coefficient,
- \(p\) is the probability of success on an individual trial,
- \(n\) is the number of trials,
- \(k\) is the number of successful trials you want to find the probability for.
Transcribed Image Text:### Educational Website Content: Binomial Probability Example
**Problem Statement (Part 4 of 4):**
Given:
- \( n = 14 \) (number of trials)
- \( p = 0.7 \) (probability of success on each trial)
- \( X = 11 \) (number of successes)
Calculate \( P(X) \), the probability of exactly 11 successes.
**Input Field:**
The input box is provided for entering the calculated probability.
**Controls:**
- A checkbox or button to submit the answer.
- A reset button to clear previous input.
**Navigation:**
- A "Continue" button to proceed to the next part or submit your work once done.
### Explanation
This problem deals with calculating the probability of a specific number of successes in a binomial distribution scenario. The binomial distribution formula is applied here to find \( P(X = 11) \), where the settings involve a fixed number of trials and a constant probability of success.
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