Business Data Model
Business Decision Models ____________________________________________________________
________________________ Question 1 (10 marks)
Sandra Enright of Techtronics Inc., an electronics supply firm, has been examining the times required for stock pickers to fill orders requested from inventory. She has determined that individual order-filling times approximately follow a normal distribution with a mean value of 3.2 minutes and standard deviation of 68 seconds.
a) What is the probability that a randomly selected order will require more than three minutes? b) What is the probability that a randomly selected order will require less than two minutes? c) What is the probability that a randomly selected order will require between two and three minutes? d) Sandra is considering a quality assurance that 95% of orders will be filled within a specified time. What time should she specify?
Question 2 (15 marks)
Gerald Black of BlackFly Airline has an exclusive contract to run flights of a four-passenger aircraft to a remote mining center. His contract requires him to fly if there are any passengers wanting to make the trip. His fixed costs per day are $400.00, his fixed costs per flight are $1,200.00, the variable cost per passenger is $25.00, and he charges $850.00 per passenger. He has tracked the number of passengers who flew with him over the past sixty days. His findings are summarized in the following table: Number of Passengers | 0 | 1 | 2 | 3 | 4 | Number of Days | 5 | 12 | 15 | 21 | 7 | Of course, he does not fly on days with zero passengers. Assume that this sample gives a good approximation to his future demand patterns. Let G be the random variable: profit on a future day. a) Calculate the Expected Value, E[ G ], Variance, 2[ G ] and standard deviation, [ G ], of his future daily profit. [Hint: You can calculate a profit corresponding to each number of
________________________ Question 1 (10 marks)
Sandra Enright of Techtronics Inc., an electronics supply firm, has been examining the times required for stock pickers to fill orders requested from inventory. She has determined that individual order-filling times approximately follow a normal distribution with a mean value of 3.2 minutes and standard deviation of 68 seconds.
a) What is the probability that a randomly selected order will require more than three minutes? b) What is the probability that a randomly selected order will require less than two minutes? c) What is the probability that a randomly selected order will require between two and three minutes? d) Sandra is considering a quality assurance that 95% of orders will be filled within a specified time. What time should she specify?
Question 2 (15 marks)
Gerald Black of BlackFly Airline has an exclusive contract to run flights of a four-passenger aircraft to a remote mining center. His contract requires him to fly if there are any passengers wanting to make the trip. His fixed costs per day are $400.00, his fixed costs per flight are $1,200.00, the variable cost per passenger is $25.00, and he charges $850.00 per passenger. He has tracked the number of passengers who flew with him over the past sixty days. His findings are summarized in the following table: Number of Passengers | 0 | 1 | 2 | 3 | 4 | Number of Days | 5 | 12 | 15 | 21 | 7 | Of course, he does not fly on days with zero passengers. Assume that this sample gives a good approximation to his future demand patterns. Let G be the random variable: profit on a future day. a) Calculate the Expected Value, E[ G ], Variance, 2[ G ] and standard deviation, [ G ], of his future daily profit. [Hint: You can calculate a profit corresponding to each number of