A survey showed that 70% of adults need correction (eyeglasses, contacts, surgery, etc.) for their eyesight. If 7 adults are randomly selected, find the probability that exactly 2 of them need correction for their eyesight. Hint, use the Binomial Distribution formula. 01 0.113 0.00357 0.025
A survey showed that 70% of adults need correction (eyeglasses, contacts, surgery, etc.) for their eyesight. If 7 adults are randomly selected, find the probability that exactly 2 of them need correction for their eyesight. Hint, use the Binomial Distribution formula. 01 0.113 0.00357 0.025
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![### Probability and Binomial Distribution
**Problem:**
A survey showed that 70% of adults need correction (eyeglasses, contacts, surgery, etc.) for their eyesight.
**Question:**
If 7 adults are randomly selected, find the probability that exactly 2 of them need correction for their eyesight.
**Hint:**
Use the Binomial Distribution formula.
**Options:**
- □ 1
- □ 0.113
- □ 0.00357
- □ 0.025
**Explanation:**
Using the Binomial Distribution formula is essential here. The binomial probability formula is:
\[ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \]
where:
- \( n = 7 \) (number of trials)
- \( k = 2 \) (number of successes we are looking for)
- \( p = 0.70 \) (probability of success on an individual trial)
- \( \binom{n}{k} \) is the binomial coefficient, calculated as \(\frac{n!}{k!(n-k)!}\)
Plugging in these values will give the probability that exactly 2 out of 7 adults need correction for their eyesight.
**Note:**
There are no graphs or diagrams in this problem, only textual information and mathematical concepts.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe9ed366a-05c2-4728-8c6d-70ad10b89152%2F480079a7-b32f-4276-92e7-4a6f8b4ca361%2Fopcid6d_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Probability and Binomial Distribution
**Problem:**
A survey showed that 70% of adults need correction (eyeglasses, contacts, surgery, etc.) for their eyesight.
**Question:**
If 7 adults are randomly selected, find the probability that exactly 2 of them need correction for their eyesight.
**Hint:**
Use the Binomial Distribution formula.
**Options:**
- □ 1
- □ 0.113
- □ 0.00357
- □ 0.025
**Explanation:**
Using the Binomial Distribution formula is essential here. The binomial probability formula is:
\[ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \]
where:
- \( n = 7 \) (number of trials)
- \( k = 2 \) (number of successes we are looking for)
- \( p = 0.70 \) (probability of success on an individual trial)
- \( \binom{n}{k} \) is the binomial coefficient, calculated as \(\frac{n!}{k!(n-k)!}\)
Plugging in these values will give the probability that exactly 2 out of 7 adults need correction for their eyesight.
**Note:**
There are no graphs or diagrams in this problem, only textual information and mathematical concepts.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 2 images
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman