Question 1. An audit conducted by the St. Aleanis Hospital has determined that 15% of all patient bills contain an error of one form or another. After spending considerable effort to improve the hospital's billing process, the administrators are convinced that things have improved. They believe that the new error rate is somewhere closer to 0.05.
a) Suppose that recently the hospital randomly sampled 10 patient bills and conducted a thorough study to determine whether an error exists. It found 3 bills errors. Assuming that managers are correct that they have improved the error rate to 0.05, what is the probability that they would find 3 or more errors in a sample of 10 bills?
b) Referring to part a, what conclusion would you reach based on the probability of finding 3 or more errors in the sample of 10 bills?
Question 2. The Weyerhauser Lumber Company headquartered in Tacoma, Washington, is one of the largest timber and wood products 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 averages per sheet are being satisfied? Comment on what this probability implies about whether you think the company is meeting the 3.5 per sheet defect rate.
Question 3. When only the value-added time is considered, the time it takes to build a laser printer is thought to be uniformly distributed between 8 and 15 hours.
a) What are the chances that it will take more than 10 value-added hours to build a printer?
b) How likely is it that a printer will require less than 9 value-added hours?
c) Suppose a single customer orders two printers. Determine the probability that the first and second printer each will require less than 9 value-added hours to complete.
Question 4. USA Today reported that the average patient cost per stay in American hospitals was $8,166. Assume that this cost is exponentially distributed.
a) Determine the probability that a randomly selected patient's stay in an American hospital will cost more than $10,000.
b) Calculate the probability that a randomly selected patient's stay in an American hospital will cost less than $5,000.
c) Compute the probability that a randomly selected patient's stay in an American hospital will cost between $8,000 and $12,000.
The solution examines probability distribution for audits and a timber company.