A manufacturer of liquid crystal displays (LCDs) is studying their production lines. The probability of sampling a defective LCD is 0.1. A sample of 5 LCDs is taken. You may assume that an LCD being defective is independent of any of the others being defective. What is the probability that exactly 4 LCDs are NOT defective? 010 2) 0.00001 3) 0.06561 4) 0.32805 5) 0.59049 6) 0.6561 7) 0.91854 8) 1 9) 5

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Question
### Analyzing Defective Liquid Crystal Displays (LCDs)

#### Problem Statement
A manufacturer of liquid crystal displays (LCDs) is conducting a study of their production lines. In this scenario:

- The probability of sampling a defective LCD is 0.1.
- A sample of 5 LCDs is taken.
- It is assumed that the defect status of one LCD is independent of any others being defective.

#### Question
What is the probability that exactly 4 LCDs from the sample are NOT defective?

#### Options
1. 0
2. 0.00001
3. 0.06561
4. 0.32805
5. 0.59049
6. 0.6561
7. 0.91854
8. 1
9. 5

##### Explanation
The problem involves using concepts from probability and statistics, specifically binomial probability distribution. The binomial distribution formula is:

\[ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \]

Where:
- \( n \) is the number of trials (LCDs sampled = 5).
- \( k \) is the number of successes (non-defective LCDs = 4).
- \( p \) is the probability of success on a single trial (probability that an LCD is not defective = 1 - 0.1 = 0.9).

By calculating the values, one can determine the probability that exactly 4 out of 5 LCDs sampled are not defective.
Transcribed Image Text:### Analyzing Defective Liquid Crystal Displays (LCDs) #### Problem Statement A manufacturer of liquid crystal displays (LCDs) is conducting a study of their production lines. In this scenario: - The probability of sampling a defective LCD is 0.1. - A sample of 5 LCDs is taken. - It is assumed that the defect status of one LCD is independent of any others being defective. #### Question What is the probability that exactly 4 LCDs from the sample are NOT defective? #### Options 1. 0 2. 0.00001 3. 0.06561 4. 0.32805 5. 0.59049 6. 0.6561 7. 0.91854 8. 1 9. 5 ##### Explanation The problem involves using concepts from probability and statistics, specifically binomial probability distribution. The binomial distribution formula is: \[ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \] Where: - \( n \) is the number of trials (LCDs sampled = 5). - \( k \) is the number of successes (non-defective LCDs = 4). - \( p \) is the probability of success on a single trial (probability that an LCD is not defective = 1 - 0.1 = 0.9). By calculating the values, one can determine the probability that exactly 4 out of 5 LCDs sampled are not defective.
Expert Solution
steps

Step by step

Solved in 2 steps

Blurred answer
Similar questions
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
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 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…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
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
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman