It will be expected that all calculations and statistical analyses will be performed on paper. These calculations and analyses should then be scanned into a PDF document. Students will upload their so

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It will be expected that all calculations and statistical analyses will be performed on paper. These calculations and analyses should then be scanned into a PDF document. Students will upload their solutions in PDF format. NOTE: Only handwritten solutions will be accepted

Question 1 (4 + 2 + 2 = 8 marks)

Jeans East is a manufacturer of designer jeans. The operations manager has requested your advice to

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help him determine the size of the new factory that the company is proposing to build. The company

wishes to investigate 3 different levels of demand (pairs of jeans per annum) from the factory:

20 000, 50 000, and 100,000. The following payoff table has been constructed:

Demand  |   Small  |  Medium  |  Large  |

20,000  |  $-75000 | $-125000 | $-175000|

50,000  |  $100000 |  $175000 |  $100000|

100,000 |  $100000 |  $225000 |  $300000|

The operations manager assess the probability of the different levels of demand as follows:

Demand  | P(x)|

20,000 | 0.3 |

50,000 | 0.5 |

100,000 | 0.2 |

a)       Calculate the expected monetary value (EMV) for each possible factory size..

Which size factory would you select to maximise the expected monetary value?

Question 1 continued

b) Calculate the Expected Value of Perfect Information (EVPI) for this decision-making scenario.

c) The operations management has discovered that the jeans can be manufactured overseas removing the

need of a factory but will incur other operating costs. The profit for each level of demand are as follows:

Demand  |  Overseas  |

20,000 |     $30000 |

50,000 |    $100000 |

100,000 |    $200000 |

Calculate the EMV for the overseas option. Should they move their operations overseas?

Question 2 (3 + 2 + 3 = 8 marks)

The time required to assemble an electronic component is normally distributed, with a mean and

standard deviation of 17.6 minutes (µ) and 4.9 minutes (σ) respectively.

a) Find the probability that a particular assembly takes between 10 and 20 minutes.

b) The fastest 10% of workers to assemble their component, receive a prize.

What is the time to beat, for a worker to receive a prize?

c) The person assembling the components works for 10 hours each day. Find the probability that they

will be able to assemble 36 electric compnents in a normal day. That is, find the probability that the

total time to assemble 36 components is less than 10 hours.

Hint: Find the average number of minutes per component.

Question 3 (4 + 3 = 7 marks)

a) The average pizza delivery times are normally distributed with a known population standard deviation

of 6 minutes. A random sample of 28 pizza deliveries is taken and has a sample mean delivery time

of 26 minutes. Find a 90% confidence interval estimate for the population mean delivery time.

b)     A certain pay television company wishes to estimate the proportion of its customers who would

purchase a pay television program guide. To do this, the company manager decides to select a random

sample of customers and note the number who would purchase a program guide. Suppose that experience

in other areas suggests that about 41% of customers will purchase a program guide.

How many customers should the company manager include in his sample if he wishes to estimate the true

proportion who will purchase the program guide correct to within 1% (0.01) with a confidence level of 99%?

Question 4 (7 marks)

A courier service advertises that its average delivery time is less than 8 hours for local deliveries. A

random sample of times for 10 deliveries to an address across town was recorded. These data are

shown here (in hours).

9, 9, 10, 6, 6, 7, 7, 7, 4, 4

Assume that the times are normally distributed. Is this sufficient evidence to support the courier’s

advertisement, at the 5% level of significance?

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