Question 1 In a semiconductor production line, a manufacture batch contains 1000 pieces of wafers. A wafer contains 81 a

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Question 1 In a semiconductor production line, a manufacture
batch contains 1000 pieces of wafers. A wafer contains 81
arrays.
(a)The number of defective arrays per wafer follows a Poisson
distribution with the mean of 5, and this number of defective
arrays per waferis counted for a random sample of 125 wafers.
Compute the probability that the average number of defective arrays
per wafer will be less than 5.5.(10 marks)
(b)Now suppose that on average the proportion of defective
wafers in a large manufacture batch is 0.1. What is the smallest
random sample of items that must be taken from the batch for the
probability to be at least 0.99 that the proportion of defective
wafers in the sample will be less than 0.13?(10 marks)