problemsheet_2

problemsheet_2 - Q1 A company conducted a survey of its...

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Q1 A company conducted a survey of its employees to determine their attitude toward a buyout of the company’s stock. Each of the company’s 1040 employees was asked whether they favored the buyout and whether they planned to retire within the next 15 years. The numbers of employees falling in the four buyout-retirement categories are shown in the following table. No Yes Totals Retire Within No 464 182 646 15 Years Yes 179 215 394 Total 643 397 1040 Favour Buyout Suppose an employee is selected at random from the company. (a) What is the probability that the employee favors a buyout? (b) What is the probability that the employee will retire within the next 15 years? (c) What is the probability that the employee favors the buyout given that he or she plans to retire within the next 15 years? (d) Is an employee’s attitude toward the buyout independent of his or her retirement plans? Q2 There are 9 fair coins and 1 two-headed coin inside a box. We perform the following coin tossing experiment. First, we randomly pick a coin from the box and then we toss the chosen coin 3 times. (a) What is the probability that the chosen coin is the two-headed coin? (b) What is the probability of getting 1 head from the coin tossing experiment? (c) What is the probability of getting 2 heads from the coin tossing experiment? (d) What is the probability distribution for the number of heads obtained from the coin tossing experiment? (e) What are the mean and the standard deviation of the distribution in part (d)? (f) If the results of the experiment are 3 heads, what is the probability that the chosen coin is two-headed? (g) Answer (f) to 2 decimal places if the chosen coin is tossed a million times and the results are all heads. (Hint: no calculation should be required) Q3 John wishes to buy a stock and hold it for one year in anticipation of capital gain. He has narrowed his choice to stocks A and B. Both stocks currently sell for $100 per share and yield $5 dividends. The following probability distributions for next year’s
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prices (x and y) have been predicted for each stock. Stock A x 75 100 125 150 175 200 p(x) 0.15 0.12 0.1 0.15 0.24 0.24 Stock B y 95 100 105 110 p(y) 0.1 0.25 0.5 0.15 Calculate the expected value and the standard deviation of the prices for a share of each stock in the next year. Which stock yields the highest expected gain? Q4 An admissions committee selects students for an MBA program. Past data show that 70% of all admitted students complete the degree program and graduate. It is also known that 50% of the graduating students scored above 500 on the Graduate Management Admissions Test (GMAT), while only 20% of the students who do not graduate scored that well. Consider a newly admitted MBA student. (a) What is the probability that she scored above 500 on the GMAT?
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This note was uploaded on 09/18/2010 for the course BBA ISOM111 taught by Professor Hu during the Fall '08 term at HKUST.

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problemsheet_2 - Q1 A company conducted a survey of its...

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