Question 9 1 pts Assume that 4% of the IC chips produced by a specific supplier are defective (I wouldn't want to have to use THAT supplier!) and that 100 of the chips are put into each package. If the number of defective chips is modeled as a Poisson RV, what is the standard deviation of this RV? Give your answer in decimal form to 1 digit of precision.
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Kumar A.
(a) In a manufacturing process, 4 % of steel rods made by a machine are out of tolerance (and therefore considered defective), the defectives occurring at random during production. If rods are packaged 100 per box, what is the probability that a given box will contain: (i) r = 0, 1, 2, 3, 4 or 5 defective rods (ii) At most, 5 defective rods? Calculate the probabilities using both the Binomial distribution and a Poisson approximation. (b) The diameter of the rods are distributed normally with mean of 2 cm and standard deviation of 0.008 cm. (i) What percentage of defectives can we expect if we set the tolerance limits at 2 ± 0.02 cm? (ii) What are the tolerance limits if 4 % of the rods are allowed to be defective?
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The manufacturing of semiconductor chips produces 2% defective chips. Assume the chips are independent and that a lot contains 1000 chips. Use normal approximation. Round your answers to 4 decimal places (e.g. 98.7654).
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