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One fifth percent of the blades produced by a blade manufacturing factory turnout to be defective. The blades are supplied in packets of 10. Use poisson distribution to calculate the approximate number of packets containing. 1)no defective blade 2)one defective blade in a consignment of 10000?
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One fifth percent of the blades produced by a blade manufacturing fact...
Calculating the Number of Packets Containing Defective Blades
1) Number of Packets with no Defective Blades
- The probability of a blade being defective is 1/5 percent, which is equivalent to 0.2%.
- Therefore, the probability of a blade not being defective is 1 - 0.2% = 99.8%.
- Since each packet contains 10 blades, the probability of a packet containing no defective blades is (0.998)^10 = 0.8187.
- To calculate the number of packets with no defective blades in a consignment of 10000, we use the Poisson distribution formula: P(X = k) = (e^(-λ)*λ^k) / k!, where λ = n*p, n = 10000 packets, p = 0.8187, and k = 0 (no defective blades).
- Plugging in the values, we get P(X = 0) = (e^(-10000*0.8187)*(10000*0.8187^0)) / 0! = 0.000045.
2) Number of Packets with One Defective Blade
- The probability of a packet containing one defective blade is 10 * 0.2% * (0.998)^9 ≈ 0.002.
- Using the Poisson distribution formula with λ = n*p, n = 10000 packets, p = 0.002, and k = 1 (one defective blade), we get P(X = 1) = (e^(-10000*0.002)*(10000*0.002^1)) / 1! = 0.0366.
Therefore, approximately 0.000045 packets will contain no defective blades, and 0.0366 packets will contain one defective blade in a consignment of 10000 packets.
1) Number of Packets with no Defective Blades
- The probability of a blade being defective is 1/5 percent, which is equivalent to 0.2%.
- Therefore, the probability of a blade not being defective is 1 - 0.2% = 99.8%.
- Since each packet contains 10 blades, the probability of a packet containing no defective blades is (0.998)^10 = 0.8187.
- To calculate the number of packets with no defective blades in a consignment of 10000, we use the Poisson distribution formula: P(X = k) = (e^(-λ)*λ^k) / k!, where λ = n*p, n = 10000 packets, p = 0.8187, and k = 0 (no defective blades).
- Plugging in the values, we get P(X = 0) = (e^(-10000*0.8187)*(10000*0.8187^0)) / 0! = 0.000045.
2) Number of Packets with One Defective Blade
- The probability of a packet containing one defective blade is 10 * 0.2% * (0.998)^9 ≈ 0.002.
- Using the Poisson distribution formula with λ = n*p, n = 10000 packets, p = 0.002, and k = 1 (one defective blade), we get P(X = 1) = (e^(-10000*0.002)*(10000*0.002^1)) / 1! = 0.0366.
Therefore, approximately 0.000045 packets will contain no defective blades, and 0.0366 packets will contain one defective blade in a consignment of 10000 packets.
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One fifth percent of the blades produced by a blade manufacturing factory turnout to be defective. The blades are supplied in packets of 10. Use poisson distribution to calculate the approximate number of packets containing. 1)no defective blade 2)one defective blade in a consignment of 10000?
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One fifth percent of the blades produced by a blade manufacturing factory turnout to be defective. The blades are supplied in packets of 10. Use poisson distribution to calculate the approximate number of packets containing. 1)no defective blade 2)one defective blade in a consignment of 10000? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about One fifth percent of the blades produced by a blade manufacturing factory turnout to be defective. The blades are supplied in packets of 10. Use poisson distribution to calculate the approximate number of packets containing. 1)no defective blade 2)one defective blade in a consignment of 10000? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for One fifth percent of the blades produced by a blade manufacturing factory turnout to be defective. The blades are supplied in packets of 10. Use poisson distribution to calculate the approximate number of packets containing. 1)no defective blade 2)one defective blade in a consignment of 10000?.
One fifth percent of the blades produced by a blade manufacturing factory turnout to be defective. The blades are supplied in packets of 10. Use poisson distribution to calculate the approximate number of packets containing. 1)no defective blade 2)one defective blade in a consignment of 10000? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about One fifth percent of the blades produced by a blade manufacturing factory turnout to be defective. The blades are supplied in packets of 10. Use poisson distribution to calculate the approximate number of packets containing. 1)no defective blade 2)one defective blade in a consignment of 10000? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for One fifth percent of the blades produced by a blade manufacturing factory turnout to be defective. The blades are supplied in packets of 10. Use poisson distribution to calculate the approximate number of packets containing. 1)no defective blade 2)one defective blade in a consignment of 10000?.
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