stats. Help needed and thanks in advance.

3. (8 Marks) The number of defective circuit boards coming off a soldering machine follows a Poisson distribution. During a specific eight-hour day, one defective circuit board was found. a) Find the probability that it was produced during the first hour of operation during that day. What would be the probability that it was produced during the last hour of operation during that day? b) Find the expected value of the time when the defective circuit board was produced? c) Given that no defective circuit boards were produced during the first four hours of opera- tion, find the probability that the defective board was manufactured during the fifth hour. 4. (7 Marks) The width of bolts of fabric is normally distributed with mean 950 mm (millimeters) and standard deviation 10 mm. a) What is the probability that a randomly chosen bolt has a width of between 947 and 958 mm? b) What is the appropriate value for C such that a randomly chosen bolt has a width less than C with probability .8531