Suppose that we have two manufacturing workers, Bob and Jane, who each produce machine parts. Bob can make an average of 5 parts of per hour, with a standard deviation of 3 parts per hour (thus a variance of 9 parts per hour squared). Jane can make an average of 6 parts of per hour, with a standard deviation of 2 parts per hour (thus a variance of 4 parts per hour squared).Let X represent the number of parts made per hour by Bob. Let Y represent the number of parts made per hour by Jane. a). Let Z represent the total number of parts made per hour by both workers. What are the expected value and variance of the total number of parts made per hour by both workers?b).Suppose the reason Bob makes fewer parts per hour with higher variability is that he is making a different type of part than Jane. Our company makes a $10 profit for each part made by Bob and $9 profit for each part made by Jane. Let W be the total profit in dollars per hour from parts created by both workers. Write out W in the form of a linear combination of X's and Y's. c). Find the combined average and variance for profit in dollars per hour created by the two workers.