MTH220 Statistical Methods and Inference

This assignment is worth 16% of the final mark for MTH220 Statistical Methods and Inference The cut-off date for this assignment is 20 October 2021 (Wednesday), 23 55 hours.You are to include the following particulars in your submission.

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 wafer is 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.
(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?

A student is working on a quiz containing 15 multiple choice questions. The probability that the student gets correct answer for a multiple choice question is