Discuss the below:
Q1. Gateway 2000, Inc., receives large shipments of microprocessors from Intel Corp. It must try to ensure that the portion of microprocessors that are defective is small. Suppose Gateway decided to test five microprocessors out of shipment of thousands them.
Suppose that if at least one of the microprocessor is defective, the shipment is returned.
a. If the Intel Corp.s shipments contains 10% defective microprocessors, calculate the probability the entire shipment will be returned.
b. if the Intel and Gateway agree that Intel will not provide more thatn 5% defective chips, calculate the probability the entire shipment will be returned.
c. Calculate the probability that the entire shipment will be kept by Gateway even though the shipment has 10% defective microprocessors.
Q2. a: The following graphic illustrates the probability distribution associated with the session-ending price of an Internet retailer's stock price. Consider the lightly shaded area under the curve. What is the probability that the price of the stock will be between $70 and $85 at the end of the trading session?
b: Consider the darker shaded sections under the curve. What is the probability that the ending stock price will be less than 25 or greater than 85? In other words, what is P(x < $25) or P(x > $85)?
Q3. Micron Electronics makes both desktops and laptop personal computers that they sell directly to the customers by phone or over internet. In addition to making the computers, Micron provides customer support via 1-800 number. Recently the manager of the service department conducted a study of the time customers spent on hold waiting for a Micron representative to become available. The data showed that the distribution of time spent on hold is approximately normal distributed, with a mean of 18 minutes and a standard deviation of 4 minutes:
a. Based on this information, what is probability that a customer will have to wait more than 11.3 minutes?
b. Considering the data collected in this study, what is the probability that a customer will wait less than 2 minutes?
c. Suppose a customer has complained to the customer service manager that she was on hold for 22 minutes. Based on the data collected in the study, how would you respond to this customer? Do you think that the customer is accurate with her claim?
d. the service manager wants to make sure (for all practical purpose) that no one waits longer that 18 minutes. Determine the standard deviation that would be required to meet this goal.
Q4. 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 the chances that it will take more than 10 value-added hours to build printer?
b. How likely is it that the printer will require fewer 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 fewer than 9 value-added hours to complete.