3100 MGMT HOMEWORK ASSIGNMENT #3 NOTE1: Questions 1-50 = 4 points each, Questions 51-100 = 13 points each NOTE3: YOU ONLY NEED TO TURN IN YOUR SCANTRONS FOR THIS ONE PROBLEM 1 (harder) You invested $10,000 in a certain stock on January 1st, 2007. By examining past movements of this stock and checking up with your broker, you estimated that the annual return for the stock (call it X and express it as a percentage), is normally distributed with mean = 10% and standard deviation 4%. On December 31st, 2007, your investment will have grown to $10,000(1 + X) and you will sell the stock. Because you are in the 33% bracket (I'm assuming you guys have money), you will owe the IRS 33% of this profit. **Question 51. What is the approximate probability that you will have to pay the IRS at least $400? a) 0% b) 70.2% c) 29.8% d) 33% e) none of the above *Question 1. What is the lowest approximate rate of return (X), which you are 90% sure you will NOT make? a) 0% b) 15.13% c) 10% d) 14% e) none of the above **Question 52. What is the lowest approximate after tax profit (in $) which you are 90% sure you will NOT exceed? a) $1513 PROBLEM 2 The Fabulous Fabrics Company runs a manufacturing facility that produces bolts of woolen fabric. A certain amount of other fibers are also woven into the wool. The proportion of those other fibers is supposed to be about 20 pounds per 1000 feet of fabric. Because of natural variations in the manufacturing process (see MGMT 3620) the other fiber content actuall varies according to a Normal Distribution with mean = 20 pounds. The standard deviation depends on "good" days and "bad" days (If the machine was properly cleaned or not). On "good" days STDEV = 0.1 pounds and on "bad" days it is = 0.15 pounds. A given bolt must be rejected by Quality Control if the content of the other fibers falls below 19.8 pounds or exceeds 20.3 pounds. Hint: In this case the Probability of (A OR B) = Probablity of A + Probability of B **Question 53. What is the approximate probability a bolt of fabric would be rejected on a "good" day? a) 0.135% b) 11.4% c) 2.275%
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b) $1000
c) $1013
d) $600
e) none of the above
d) 2.4%
e) none of the above
*Question 2. What is the approximate probability a bolt of fabric would be rejected on a "bad" day? a) 9.12% PROBLEM 3 Suppose it is known that customers in a retail store will purchase $25 on average per visit, with a standard deviation of $8. Assume also that the distribution of purchases is normal. *Question 3. What is the approximate probability that a randomly selected customer will spend between $15 and $35? a) 10.56% b) 89.43% c) 78.87% d) 50% e) none of the above *Question 4. What is the approximate dollar amount such that 80% of customers will spend at least that much? a) $25 b) $29 c) $35 d) $40 e) of none the above *Question 5. What is the approximate dollar amount (rounded up or down to the closest dollar) such that 75% of customers will spend no more than this amount? a) $30 PROBLEM 4 The weekly demand for Ford cars is down to an average of 50,000 cars (normally distributed) with a standard deviation of 14,000 cars. *Question 6. What is the approximate probability that Ford will sell between 2.4 and 2.7 million cars this year? a) 94.63% a) 82568 cars PROBLEM 5 An Oil company supplies its customers with barrels that contain about 55 gallons of oil apiece. The amount of oil in the barrels fluctuates with mean = 55 gallons and standard deviation = 0.5 gallon. *Question 8. What is the approx. probability that a given barrel will be short by 1 gallon or more? a) 0% b) 95.3% c) 4.8%
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b) 11.4%
c) 2.275%
d) 2.4%
e) none of the above
b) $31
c) $35
d) $29
e) none of the above
b) 39.17% b) 17431 cars
c) 55.46% c) 32058 cars
d) 16.28% d) 64,000 cars
e) none of the above e) none of the above
*Question 7. There is a 1% chance Ford car weekly sales will exceed what number?
d) 2.3%
e) none of the above
*Question 9. What is the approximate Z-score for 54 gallons? a) -2 a) 54 b) -1.67 b) 55 c) 1.67 c) 56.37 d) 2 d) 99.7 e) none of the above e) none of the above *Question 10. Approximately up to how many gallons would each of 99.7% of the barrels contain?
Improved quality control procedures at the filling station of the company reduced the standard deviation to 0.25 gallons. *Question 11. Approximately how many barrels out of 100,000 will be short by 1 gallon or more now ? a) 0 PROBLEM 6 Consider the Personnel.xls example posted on Blackboard. It is the case of a company that gives a test to job applicants. From past experience, the average score of applicants has been 525 points with a standard deviation of 55 points. The company automatically hires anybody with a score >= 600 and rejects automatically anybody with a score <= 425. *Question 12. Approximately what percent of the applicants is being automatically hired? a) 99.7% a) 99.7% b) 8.63% b) 8.63% c) 3.45% c) 3.45% d) 15% d) 15% e) 10% e) 10% *Question 13. Approximately what percent of the applicants is being automatically rejected? b) 3 c) 5 d) none of the above e) can't tell
The company now decides to start hiring automatically 15% of all applicants and reject automatically 10% of all applicants based on that same test. *Question 14. What should be approximately the new upper score that applicants would have to get in order to be hired automatically under this new policy? a) 582 b) 455 c) 600 d) 525 e) none of the above *Question 15. What should be approximately the new lower score that applicants would have to get in order to NOT be rejected automatically under this new policy? a) 582 b) 455 c) 600 d) 525 e) none of the above
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