2004-Fall-Midterm

2004-Fall-Midterm - More PastPaper:...

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Unformatted text preview: More PastPaper: http://ihome.ust.hk/~cs_gxx ISMT111 Business Statistics Midterm Examination For sections 3, 4, 5 & 6 only 15th October 2004 Directions 1) Answer ALL FIVE questions. Marks are shown in square brackets. 2) There are 4 pages in this examination paper. Check to make sure you have a complete set and notify the invigilator immediately if part of it is missing. 3) Key formulas and Statistical tables are provided separately. 4) Calculator may be used in this examination. ht tp :// ih om e. us t.h k/ ~c s_ gx x/ 5) You are given TWO HOURS to complete this examination. Do not begin until you are told to do so. 1 More PastPaper: http://ihome.ust.hk/~cs_gxx Question 1: [22 Marks] Airlines often intentionally overbook flights knowing that not everyone who purchased a ticket for the flight will actually show up. Suppose that there is a 98% chance that a passenger with a ticket will actually show up for the flight. Consider a particular flight has 85 seats and the airline sold 88 tickets for the flight. (a) What assumption is needed in order to claim that the number of passengers showing up is a binomial random variable? Hereafter, you can answer the following parts with such an assumption. (b) What is the expected number of passengers that will show up? (c) Suppose that all tickets are purchased for $375. If more passengers show up than there are seats available for the flight the airline will have to pay $1000 to each passenger without a seat. Assume that the airline keeps the money from tickets purchased even if the passenger doesn't get on the flight. (Hint: Do NOT use normal approximation in part (c).) (i) What is the probability that the airline will not need to pay any money to the passengers for overbooking? (ii) What is the distribution of the airline net revenue (Hint: Net revenue=revenue minus the payout for overbooking)? (iii)What is the airline expected net revenue? (iv) Give a reason why normal approximation may give a significant error for the computations of the airline net revenue. Question 2: [22 Marks] You have mineral rights on a piece of land that has a probability of 0.1 of containing oil. If you test drill and it does contain oil, the payoff is $200,000,000. However, it costs $10,000,000 to perform the drilling. Before test drill you can consult a geologist who can assess the promise of the land. She can tell whether your prospects are ‘good’ or ‘not good’, but she is not a perfect predictor. If there is oil, the conditional probability that she will say that the prospects are good is 0.9. If there is no oil, the conditional probability that she will say that prospects are not good is 0.85. The geologist charges $700,000 as her consulting fee. gx x/ (a) Suppose you consult the geologist and she says that the prospects are ‘good’. (i) What is the probability that you will strike oil if you test drill? om e. us t.h k/ ~c s_ (ii) What is the expected profit if you test drill? 2 :// ht tp (i) What is the probability that you will strike oil if you test drill? (ii) What is the expected profit if you test drill? ih (b) Suppose you consult the geologist and she says that the prospects are ‘not good’. More PastPaper: http://ihome.ust.hk/~cs_gxx (iii) What is the expected profit you do not test drill? (iv) Should you test drill in this case? (c) Should you consult the geologist? Question 3: [16 Marks] A survey was conducted of 1200 people (600 Men and 600 Women) to see what types of movies men and women like to see at the cinema. Each person was asked if they would prefer to see an Action/Horror Movie or a Funny/Romantic Movie. 800 people said they preferred Action/Horror Movies to Funny/Romantic Movies. 300 Women said they preferred Funny/Romantic Movies. (a) (b) (c) Using the information above, construct an appropriate Contingency table. What is the probability that a person prefers a Funny/Romantic Movie? Given that a person prefers Action/Horror movies what is the probability that the person is a woman. Assume that probabilities obtained from the contingency table represent that of a larger population. Suppose also that the preference of each person is independent of one another. (d) (e) What is the probability that a man and a woman will have the same preference in movies? What is the probability that two men will have the same preference? Question 4: [20 Marks] In an attempt to better manage time, a customer service officer recorded the time required, in minutes, to respond to each telephone call in a randomly selected day. ht tp :// ih om e. us t.h reasonable? Explain your answer. k/ ~c s_ sampled calls are 241.6 and 2902.56. (a) Calculate the sample mean and standard deviation of the 45 sampled calls. (b) To compare the distribution of the length of calls in the three types, the following boxplots were produced. Describe and compare the three distributions. Do you think the assumption of normal distribution for the three lengths of phone calls gx x/ The telephone calls were classified by type into ‘Information’, ‘Sales’ and ‘Service’. In the day selected, 13, 17 and 15 calls were recorded for Information, Sales and Service types respectively. The sum and the sum of squares of the lengths of these 45 3 More PastPaper: http://ihome.ust.hk/~cs_gxx (c) Based on the boxplots, produce a rough sketch of the histogram of the lengths for the Sales type. (d) From the above boxplots, do you know exactly which type of call has the highest average length? If so, what is it? (e) Another sample of 7 randomly selected phone calls from the type ‘Other’ was collected. The sample mean and standard deviation of these 7 observations are 2.79 and 1.78 respectively. Combining the four types together, calculate the combined sample mean and standard deviation of the 52 phone calls. Question 5: [20 Marks] A bank sells three mutual funds: high-risk, average-risk, and low-risk. The bank finds twice as many average-risk funds than the low-risk funds, while the sale of high-risk funds is about the same as low-risk funds. The chance of a positive return at year's k/ ~c s_ om e. us t.h (c) Suppose the daily return of investing in a high-risk fund is normally distributed with mean 0.05% and standard deviation 1.8%. (i) What is the chance of having positive return of investing in the high-risk gx x/ end is 20% for high-risk funds, 15% for average-risk funds, and 10% for low-risk funds. An investor purchased one of these mutual funds from the bank a year ago. (a) What is the probability that he or she receive a positive return on the fund bought? (b) If he or she has a positive return, what is the probability that he or she bought the high-risk fund? ht tp :// ih fund in a single day? (ii) Find a ‘cut loss’ value b so that 98% of the time we will have a return greater than b. 4 ...
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This note was uploaded on 02/27/2010 for the course ISOM ISOM111 taught by Professor Anthonychan during the Spring '09 term at HKUST.

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