Business Statistics

Part A 14 MARKS

1. You are presented with investment opportunities A and B. The potential profits and associated probabilities for both opportunities are shown in the table below. 5 MARKS 9 MARKS

Probability Investment A

Profit Investment B

Profit

0.4 $50 $100

0.6 $200 $150

a. For opportunity A, the expected monetary value equals _____________ and the standard deviation equals ___________ (2 marks)

b. For opportunity B, the expected monetary value equals _____________ and the standard deviation equals ___________ (2 marks)

c. Which investment opportunity would you choose and why? (1 mark)

2. Suppose the Ontario Lottery and Gaming Corporation is planning a new game for the 2016 holiday season called the Jolly Stuffer. Total instant winnings of $34.8 million will be available in 70 million $1 tickets. Ticket prices will range from $1 to $1 000. The table below shows the prizes along with the probabilities of winning each prize. SHOW YOUR WORK. 3 MARKS

Prize (x) Probability P(x)

$1 000 .00002

100 .00063

20 .00400

10 .00601

4 .02403

2 .08877

1 .10479

a. What is the probability of not winning any prize? _________________ (1 mark)

b. On average, how much would a person playing this game for a long time expect to lose per game? ___________ (2 marks)

3. Statistics Canada recently reported that approximately 7% of all workers in Canada are unemployed. In conducting a random telephone survey, what is the probability of getting 2 or fewer unemployed Canadian workers in a sample of 20? SHOW YOUR WORK_________ 2 MARKS

4. Outsourcing overseas has become more frequently used by North American companies. However, outsourcing is not without its problems. A survey by Purchasing magazine recently indicated that 20% of companies that outsource overseas use a consultant. Suppose we randomly select 15 companies that outsource. USE BINOMIAL TABLE B.1 in your text to answer these questions. 4 MARKS

a. What is the probability that exactly 5 companies that outsource overseas use a consultant? _______

b. What is the probability that more than 9 companies that outsource use a consultant? ______

c. What is the probability that none of the companies that outsource use a consultant? __________

d. What is the probability that between 4 and 7 (inclusive) companies that outsource overseas use a consultant? ________

Part B – Chapter Seven 16 MARKS

5. Suppose that the assembly time for some plastic component ranges from 27 to 35 seconds (note: this is a change from the original assignment posted which stated 27 to 30 seconds), and that assembly times are uniformly distributed. 6 MARKS

a. Draw the probability distribution of assembly times clearly identifying all relevant values.

b. The mean of the distribution equal to ________ and the standard deviation is equal to __________.

c. What is the probability that a given assembly will take between 30 and 35 seconds?

d. What is the probability that a given assembly will take no more than 30 seconds?

e. What is the probability that a given assembly will take exactly 30 seconds?

You must show your work for all the following questions

6. A study was done to determine stress levels that students have while taking exams. The stress level was found to be normally distributed with a mean of 8.2 and a standard deviation of 1.34. What is the probability that at your next exam, you will have a stress level between 9 and 10? ________________

Draw a diagram showing the x values, z values and area of the probability you are solving for. 3 MARKS

7. You are the manager at a new toy store and want to determine how many Monopoly games to stock in your store. The expected value of the number of Monopoly games that sell per month is 22 with a standard deviation of 6. Assume that this distribution is normal. If you stock 45 games per month, should you feel confident about not running out? Explain. 1 MARK

8. The seasonal output of a new experimental strain of pepper plants was carefully weighed. The mean weight per plant was found to be 15.0 pounds, and the standard deviation of the normally distributed weights was 1.75 pounds. If we randomly select 200 plants from this new strain of plants, how many plants (not what percent) would we expect to weigh between 13 and 16 pounds? ___________ 1 MARK

9. A manufacturer fills cereal boxes using a machine. It labels the boxes as “16 oz.” But since no packaging process is perfect, there will always be minor variations in the actual weight. Experience with the machine indicates that the weights are distributed normally with a standard deviation of 0.2 oz. 5 MARKS

a. If the machine is set at exactly 16 oz. then half of the boxes are likely to be underweight making consumers unhappy and possible lawsuits. To prevent this, the manufacturer adjusts the machine so that, on average, 16.3 oz. of cereal gets put into each box. Approximately what percent of the boxes will still be underweight? Draw a diagram showing all relevant x and z values, and the area of underweight boxes. (3 marks)

b. The company’s lawyers warn that the percent of underweight boxes is still too high when the machine is adjusted to 16.3 oz. They insist that, to be on the safe side, no more than 3% of the boxes should be underweight. So the company needs to set the machine at a higher mean weight. What mean setting is required? (1 mark)

c. The company president believes that they should not be giving away this much free cereal. She believes the machine should be set no higher than 16.2 oz. and still only have 4% underweight boxes. The only way to accomplish this is to reduce the standard deviation. What standard deviation needs to be achieved? (1 mark

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