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The Weyerhauser Lumber Company headquartered in Tacoma, Washington, is one of the largest timber- and wood-product companies in the world. Weyerhauser manufactures plywood at one of its Oregon plants. Plywood contains minor imperfections that can be repaired with small “plugs.” One customer will accept plywood with a maximum of 3.5 plugs per sheet on average. Suppose a shipment was sent to this customer, and when the customer inspected two sheets at random, 10 plugged defects were counted. What is the probability of observing 10 or more plugged defects if in fact the 3.5 average per sheet is being satisfied? Comment on what this probability implies about whether you think the company is meeting the 3.5 per sheet defect rate.
When things are operating properly, E-Bank United, an Internet bank, can process a maximum of 25 electronic transfers every minute during the busiest periods of the day. If it receives more transfer requests than this, then the bank’s computer system will become so overburdened that it will slow to the point that no electronic transfers can be handled. If during the busiest periods of the day requests for electronic transfers arrive at the rate of 170 per 10-minute period on average, what is the probability that the system will be overwhelmed by requests? Assume that the process can be described using a Poisson distribution.