QUESTION THREE (20 marks) a) When is it permissible to use the Poisson distribution as an...

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QUESTION THREE (20 marks) a) When is it permissible to use the Poisson distribution as an approximation to the binomial distribution? [1 mark] b) A factory produces an electronic component. The probability that a component is defective is 0.05. The components are packed in boxes of 24. i.) ii.) iii.) Calculate the probability that a box picked at random contains exactly 22 components. All boxes are inspected and a box is rejected if it contains fewer than 22 components. Calculate the probability that a box picked at random is rejected. The factory produces 80 boxes per day over a long period of time. Estimate the standard deviation of the number of boxes rejected per day. non defective [2 marks] non defective [3 marks] mean and the [3 marks] c) Defective spots occur at random in the manufacture of a cable at an average of one in 100m. Lengths of this cable are wound onto drums. Each drum carries 50m. A contractor buys 5 such drums. Find the probability that exactly two of these drums have no weak spots. [5 Marks] d) Determine the cumulative distribution function for the distribution given as; 0≤x≤1 f(x)=2-x, 1<x<2 0, elsewhere e) 5% of items produced in a factory are defective. A random sample of 1000 items produced in the factory are inspected. Find the probability that between 35 and 65 items are defective. [3 Marks] [3 marks] QUESTION THREE (20 marks) a) When is it permissible to use the Poisson distribution as an approximation to the binomial distribution? [1 mark] b) A factory produces an electronic component. The probability that a component is defective is 0.05. The components are packed in boxes of 24. i.) ii.) iii.) Calculate the probability that a box picked at random contains exactly 22 components. All boxes are inspected and a box is rejected if it contains fewer than 22 components. Calculate the probability that a box picked at random is rejected. The factory produces 80 boxes per day over a long period of time. Estimate the standard deviation of the number of boxes rejected per day. non defective [2 marks] non defective [3 marks] mean and the [3 marks] c) Defective spots occur at random in the manufacture of a cable at an average of one in 100m. Lengths of this cable are wound onto drums. Each drum carries 50m. A contractor buys 5 such drums. Find the probability that exactly two of these drums have no weak spots. [5 Marks] d) Determine the cumulative distribution function for the distribution given as; 0≤x≤1 f(x)=2-x, 1<x<2 0, elsewhere e) 5% of items produced in a factory are defective. A random sample of 1000 items produced in the factory are inspected. Find the probability that between 35 and 65 items are defective. [3 Marks] [3 marks]

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The detailed answer for the above question is provided below a The Poisson distribution can be used ... View the full answer