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In a certain manufacturing process 5% of the tool produced on out to be defective find probability in a simple of 40 tools almost 2 will be defective?
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Calculating the Probability of Defective Tools
To calculate the probability of having almost 2 defective tools in a sample of 40, we can use the binomial probability formula. In this case, the probability of a tool being defective is 5%, or 0.05.
Binomial Probability Formula:
P(X = k) = (n choose k) * p^k * (1-p)^(n-k)
Where:
- n is the total number of trials (40 tools in this case)
- k is the number of successful trials (defective tools)
- p is the probability of success in each trial (0.05 for defective tools)
Calculating the Probability:
1. Calculate the probability of having exactly 2 defective tools:
P(X = 2) = (40 choose 2) * 0.05^2 * 0.95^38
2. Calculate the probability of having exactly 1 defective tool:
P(X = 1) = (40 choose 1) * 0.05^1 * 0.95^39
3. Add the probabilities of having 1 and 2 defective tools to get the total probability of almost 2 defective tools:
P(almost 2 defective tools) = P(X = 1) + P(X = 2)
4. Convert the probabilities into percentages for easier interpretation.
Interpreting the Results:
By calculating the probabilities using the binomial formula, we can determine the likelihood of having almost 2 defective tools in a sample of 40. This information can be useful for quality control and decision-making processes in the manufacturing industry.
To calculate the probability of having almost 2 defective tools in a sample of 40, we can use the binomial probability formula. In this case, the probability of a tool being defective is 5%, or 0.05.
Binomial Probability Formula:
P(X = k) = (n choose k) * p^k * (1-p)^(n-k)
Where:
- n is the total number of trials (40 tools in this case)
- k is the number of successful trials (defective tools)
- p is the probability of success in each trial (0.05 for defective tools)
Calculating the Probability:
1. Calculate the probability of having exactly 2 defective tools:
P(X = 2) = (40 choose 2) * 0.05^2 * 0.95^38
2. Calculate the probability of having exactly 1 defective tool:
P(X = 1) = (40 choose 1) * 0.05^1 * 0.95^39
3. Add the probabilities of having 1 and 2 defective tools to get the total probability of almost 2 defective tools:
P(almost 2 defective tools) = P(X = 1) + P(X = 2)
4. Convert the probabilities into percentages for easier interpretation.
Interpreting the Results:
By calculating the probabilities using the binomial formula, we can determine the likelihood of having almost 2 defective tools in a sample of 40. This information can be useful for quality control and decision-making processes in the manufacturing industry.
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In a certain manufacturing process 5% of the tool produced on out to be defective find probability in a simple of 40 tools almost 2 will be defective?
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In a certain manufacturing process 5% of the tool produced on out to be defective find probability in a simple of 40 tools almost 2 will be defective? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about In a certain manufacturing process 5% of the tool produced on out to be defective find probability in a simple of 40 tools almost 2 will be defective? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a certain manufacturing process 5% of the tool produced on out to be defective find probability in a simple of 40 tools almost 2 will be defective?.
In a certain manufacturing process 5% of the tool produced on out to be defective find probability in a simple of 40 tools almost 2 will be defective? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about In a certain manufacturing process 5% of the tool produced on out to be defective find probability in a simple of 40 tools almost 2 will be defective? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a certain manufacturing process 5% of the tool produced on out to be defective find probability in a simple of 40 tools almost 2 will be defective?.
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