In the production of metal plates for an assembly, it is known from past experience that 5% of the plates do not meet the length requirement. Also, from historical records, 3% of the plates do not meet the width requirement. Assuming that there are no dependencies between the processes that make the length and those that trim the width. (a) What is the probability of producing a plate that meets both the length and width requirements? (b) What proportion of the parts will not meet at least one of the requirements? (c) What proportion of parts will meet neither length nor width requirements? (d) Suppose the operations that produce the length independent. If the length does not satisfy the requirement, it causes an improper positioning of the part during the width trimming and thereby increases the chances of nonconforming width. From experience, it is estimated that if the length does not conform to the requirement, the chance of producing nonconforming widths is 60%. Find the proportion of parts that will not conform to either the length or the width and the width are not requirement. (e) In part (a), are events Land W mutually exclusive?