3. a. Bits are transmitted through a digital transmission channel. The probability of receiving these transmitted bits, in error, is 0.1. Assume that the transmission trials are independent. i. Let X be the number of bits received in error in the next 6 bits transmitted. Determine the probability that X is not more than 2 . [5 marks] ii. Let Y be the number of bits received in error in the next 900 bits transmitted. Estimate the probability that the number of bits received in error is at least 106. [5 marks] b. The minimum time taken for a data collection operator to fill up an electronic form is 7 minutes. Records have shown that the time taken is normally distributed with a mean of 8 minutes and a standard deviation of 2.5 minutes. Assume that the time taken to fill up the forms is independent. i. Determine the appropriate distribution of the average time taken to fill up TEN (10) randomly electronic forms. [2 marks] ii. Find the probability that the average time taken to fill up the TEN (10) forms meets the requirement of minimum time. [4 marks] iii. Evaluate the minimum time required such that the probability of sample mean meeting this requirement is 98%. [4 marks]