) Suppose the percentage of those completing a master's degree is 42%. In a random sample of 9 master's degree students, what is the probability that exactly 5 will complete their degrees?
) Suppose the percentage of those completing a master's degree is 42%. In a random sample of 9 master's degree students, what is the probability that exactly 5 will complete their degrees?
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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Question
![**Problem Statement:**
Suppose the percentage of those completing a master's degree is 42%. In a random sample of 9 master's degree students, what is the probability that exactly 5 will complete their degrees?
**Explanation:**
This problem involves calculating probabilities using the binomial distribution, where:
- The number of trials \( n \) is 9.
- The probability of success (completing the degree) \( p \) is 0.42.
- We are looking for the probability of exactly 5 successes.
The probability of exactly \( k \) successes in \( n \) independent Bernoulli trials is given by the binomial probability formula:
\[ P(X = k) = \binom{n}{k} \cdot p^k \cdot (1-p)^{n-k} \]
Where:
- \( \binom{n}{k} \) is the binomial coefficient, calculated as \( \frac{n!}{k! (n-k)!} \).
- The formula calculates the likelihood of getting exactly 5 students completing their master's out of 9.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3d8d143f-a211-410b-93d7-c25b2730a251%2F4fd06cde-563a-4a34-9aca-3fc96732422d%2F358lam_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Suppose the percentage of those completing a master's degree is 42%. In a random sample of 9 master's degree students, what is the probability that exactly 5 will complete their degrees?
**Explanation:**
This problem involves calculating probabilities using the binomial distribution, where:
- The number of trials \( n \) is 9.
- The probability of success (completing the degree) \( p \) is 0.42.
- We are looking for the probability of exactly 5 successes.
The probability of exactly \( k \) successes in \( n \) independent Bernoulli trials is given by the binomial probability formula:
\[ P(X = k) = \binom{n}{k} \cdot p^k \cdot (1-p)^{n-k} \]
Where:
- \( \binom{n}{k} \) is the binomial coefficient, calculated as \( \frac{n!}{k! (n-k)!} \).
- The formula calculates the likelihood of getting exactly 5 students completing their master's out of 9.
Expert Solution
Step 1: Given information
n=sample size=9, p=42%
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