For Questions 1 to 6, refer to the following information

Transcription

1 For Questions 1 to 6, refer to the following information The Box-and-Whisker plots show the results of the quiz and test for QMS102 in Fall2010 Question 1. Calculate the mode for the quiz result of QMS102 in Fall2010 Question 2. Describe the distribution for the test result of QMS102 in Fall 2010 A. Normally distributed B. Negatively skewed C. Positively skewed D. No skewness E. Symmetrical Question 3. Select the most appropriate measure of central tendency to describe the quiz result. A. mean B. median C. mode D. standard deviation E. interquartile range Question 4. Select the most appropriate measure of central tendency to describe the test result. A. mean B. median C. mode D. standard deviation E. interquartile range 1

2 Question 5. Compute the standard deviation for the quiz result based on the box-and-whisker plot. A B C D E. Cannot be computed Question 6. Can we calculate the interquartile range for the test result based on the box-andwhisker plot? A. Yes B. No Question 7. According to the Ryerson Accounting Firm, the chances of your tax return being audited by Revenue Canada are about 11 in 1000 if your income is less than $60,000. The chances increase to 24 in 1000 if your income is more than $60,000. You are presently employed by an accounting firm and have prepared tax returns for 47 clients with income under $60,000 and for 68 clients with income over $60,000. a. Determine the probability that at least one of the clients with income under $60,000 will be audited. b. Determine the probability that at least 5 of the clients with income over $60,000 will be audited. Question 8. The length of life of a certain type of DVD is normally distributes with a mean of 6.0 years and a standard deviation of 1.3 years. Each DVD sold is under guarantee and is replaced if its length of life is less than guaranteed length of life. What period of time should the manufacturer of this type of DVD give as a guarantee if he is willing to replace no more than 6% of the DVDs? Question 9. Ryerson Company has its annual sales convention in Hong Kong each year for its top sellers. The Toronto office of the firm has kept records of the trip cost over the past years. The mean cost per person has been $4400 with a standard deviation of $300. The distribution of the cost per person has been normally distributed. a. If only one person from the Toronto office is eligible to attend this year convention, what is the probability that the cost will be between $4000 and $5000? b. If nine people from the Toronto office are eligible, what is the probability that the average cost of these five people will exceed $4500? 2

3 For Questions 10 to 20, refer to the following information Forty people were each asked how many times they ate at their favorite restaurant in the last 12 months. The results are summarized in the Stem-and- Leaf display below. Stem (tens) Leaves Question 10. Calculate the mean Question 11. Calculate the sample standard deviation Question 12. Calculate the interquartile range Question 13. Calculate the left inner fence Question 14. Calculate the right inner fence Question 15. Calculate the smallest value for the left whisker Question 16. Calculate the largest value for the right whisker Question 17. Calculate the left outer fence 3

4 Question 18. Calculate the right outer fence Question 19. Determine the suspect outlier(s) Question 20. Determine the outlier(s) Question 21. The mean time to download a game from Internet was 8 minutes. Suppose that the download time was normally distributed with standard deviation of 2 minutes. If you select a random sample of 30 download times. a. What is the probability that the sample mean is less than 7.5 minutes? b. What is the probability that the sample mean is between 7 minutes and 9 minutes? c. There is an 80% chance that the sample mean is between what two values symmetrically distributed around the population mean? d. the probability is 0.9 that the sample mean is less than what value? Question 22. The following stem-and-leaf display shows the amount in dollars spent on groceries for a sample of 25 customers at Yes Frills in the first week of September The amount spent on groceries at Food Basic first week of September 2012 Stem (0 s) Leaf a. The suspect outlier(s) b. The outlier(s) 4

5 Question 23 A Go Bus from Brampton is scheduled to arrive at Union Station at 20 minutes past the hours, but the actual times of arrival are normally distributed about the mean of 24 minutes past the hours with a standard deviation of 4.3 minutes. Determine the probability that the Go bus from Brampton will arrive a. between 11:15A.M and 11:40 A.M b. late but before 2:30 P.M Question 24. Major software manufacturers offer a help line that allows customers to call and receive assistance in solving their problems. However, because of the volume of calls, customers frequently are put on hold. One software manufacturer claims that only 24% of calls are put on hold. Suppose that 80 customers call. a. Define the variable X b. Determine i.the probability that more than 20 of them put on hold. ii. the probability that less than 60 of them will not put on hold iii. the mean and the standard deviation. Question 25. Metro paper reported that 38% of working adults spend less than $300 each month for on line shopping and 27% of working adults spend at least $600 each month for on line shopping. a. Among 150 randomly selected working adults, what is the probability that less than 95 of them spend at least $300 each month for on line shopping? b. Among 110 randomly selected working adults, what is the probability that more than 78 of them spend less than $600 each month for on line shopping? c. Among 200 randomly selected working adults, what is the probability that less than 60 of them spend at least $300 but less than $600 each month for on line shopping? d. Among 140 randomly selected working adults, what is the probability that at most 95 of them spend at least $300 each month for on line shopping? 5

6 Question 26. Assume that the mean hourly cost to operate a commercial airplane follows the normal distribution with a mean $2280 per hour and a standard deviation of $165. a. What is the minimum amount of the operation cost for the highest 8 percent of the airplanes? b. The monthly sales of mufflers in downtown Toronto follow the normal distribution with a mean of 1,056 and a variance of 186. The manufacturer would like to establish inventory levels such that there is only a 5% chance of running out of stock. Where should the manufacturer set the inventory levels? Question 27. The normal weekly demand of a certain perishable product sold by Ryerson Inc. is given by the following distribution Demand Probability b 0.3 b a a a The product costs Ryerson $5 each. The product sells for $12 each. If not sold by the end of the week, the leftover units must be scrapped. The supplier only has 12, 14 or 15 units for Ryerson to purchase. How many would you recommend Ryerson purchase based on expected profit? Assume b=2a Question 28. Ryerson Pink Inc. plans to install a new ice-cream dispensing unit in one of three store locations. The company figures that the probability of a unit being successful in location A is 7/8 and the annual profit in this case is $120,000. If it is not successful there will be losses of $76,800. At the location B the probability of succeeding is ½ but the potential profit and loss are $365,000 and $198,000 respectively. At the location C the probability of a unit being successful is 0.35 and annual profit is $350,000, the probability of 0.45 will be at a loss of $95,000 and the probability of 0.2 will be at breakeven. a. Where should the company locate to maximize expected profit? b. Which location is less risky, i.e has the lowest relative variability? Question 29. Complaints about an Internet brokerage firm occur at a rate of five per day. Determine the probability that the firm receive a. at least 10 complaints in a day. b. at most 25 complaints in a 5-day period c. between 12 and 18 complaints (Inclusive) in a 2-day period. d. more than 3 complaints in a half-day period 6

7 Question 30. Ryerson Bank has recently performed a detailed analysis of its customers. Some of the results are mentioned below. Thirty-five percent of the customers prefer to use the drive-through ATM. Twentytwo percent use the ATM next to the bank entrance. Twenty-eight percent prefer to use the service of a human teller, while the remainders do their banking online. If during the morning, 42 customers made banking transactions, what is the probability that a. at least 10 customers would use the ATM next to the bank entrance? b. at least 3 customers would use the on-line banking? c. less than 35 customers would not use on-line banking? Question 31. The number of accidents that occur at a busy intersection is Poisson distributed with a mean of 3.5 per week. Determine the probability of the following events. a. No accidents in one week. b. Five or more accident in one week. c. One accident today. d. at least 6 in two-week period e. less than 3 in 5-day Question 32. Because of the relatively high interest rates, most consumers attempt to pay off their credit card bills promptly. However, this is not always possible. Analysis of the amount of interest paid monthly by a Visa cardholder reveals that the amount is normally distributed with a mean of $29.53 and standard deviation of $6.79. a. Define the variable X b. Determine the probability of a Visa cardholder pay i. at least $35.00 in interest. ii. between $28.40 and $32.90 in interest iii. less than $30 or more than $50 in interest iv. within $10 of the mean in interest c. What interest payment is exceeded by only the highest 25% of the Visa cardholders? 7

8 Question 33. The number of users of an automatic banking machine is Poisson distributed. The mean number of user per 5-minute interval is 1.5. Determine the probability of the following events. a. No users in the next 5 minutes. b. Five or fewer users in the next 15 minutes. c. At least three users in the next 10 minutes. d. at least seven users in the next 24 minutes Question 34. Ryerson, a tire manufacturer, wants to select one of the feasible designs for a few longer-wearing radial tire. The manufacturing cost of each type of tire is shown below. Tire Design Fixed Cost/year Variable Cost W $42,600 $28 X $68,800 $20 Y $52,800 $24 Z $135,400 $17 There are four possible levels of annual demand: 4,000 tires, 6,000tires, 8,000 tires and 10,000 tires. The respective probabilities are 0.30, 0.25, 0.4, and The selling price will be $74 for W, $72 for X, $ 70 for Y and $75 for Z. a. Calculate the expected profit for i. Tire Design W ii.tire Design X iii. Tire Design Y iv.tire Design Z b. Based on expected profit, which design should be produced? Question 35. You can insure a $50,000 diamond for its total value by paying a premium of D dollars. If the probability of theft in a given year is estimated to be 0.01,what premium should the insurance company charge if it wants the expected gain to equal $1000? Question 36. The normal weekly demand of a certain perishable product sold by Ryerson Inc. is given by the following distribution Demand Probability The product costs Ryerson $9 each. The product sells for $16 each. If not sold by the end of the week, the leftover units must be scrapped. The supplier only has 23, 24 or 25 units for Ryerson to purchase. How many would you recommend Ryerson purchase based on expected profit? 8

9 Question 37. During a normal weekday, customers arrive randomly at an average rate of 48 per hours for the morning time period of 9:30 A.M to 12 noon. The customer arrival jumps to 114 per hour during the lunch period of 12:00 noon to 1:30 P.M. The customer arrive rate drops to 59 per hour for the afternoon period of 1:30P.M to 4:00 P.M a. Define the variable X b. Determine the probability that there will be i. more than 125 customers on a typical morning period. ii. at least 150 customers on a typical lunch period. Question 38. Ryerson Inc. conducted a survey regarding the length of time spent in the Shopper Good Mart. The report indicates that a customer spent an average of 37 minutes with a variance of 81 minutes 2 in the store. The length of time spent in the Shopper Good Mart is normally distributed. a. What is the probability that a randomly selected customer will spend between 35 minutes and 1 hour in the Shopper Good Mart? b. What is the probability that a randomly selected customer will spend less than 25 minutes or more than 1 hour in the Shopper Good Mart? c. What is the probability that a randomly selected customer will spend at most 1 hour in the Shopper Good Mart? d. What is the probability that a randomly selected customer will spend within 12 minutes of the mean in the Shopper Good Mart? Question 39. Judging from recent experience, 5 percent of the computer keyboards produced by an automatic, high-speed machine are defective. What is the probability that out of six keyboards selected at random, exactly zero keyboards will be defective? A B C D E. None of the above Question 40. The mean of a normally distributed group of weekly incomes of a large group of executives is $1,000 and the standard deviation is $100. What is the z-score for an income of $1,100? A B C D E. None of the above 9

10 Question 41. The statistical report shows that the average amount of time spent by each customer per week on online shopping is 1 hour 20 minutes with a variance of 1225 minutes 2. Assume that the data are normally distributed. a. Calculate the minimum time spent by the highest 4% of the customers on online shopping in the first week of December. b. Calculate the probability that 9 randomly chosen customers will have a mean amount of time spend on on-line shopping between 35 minutes and 65 minutes in the second week of December. c. Calculate the probability that a selected customer will spend less than 40 minutes or at least 1hour and 30 minutes in the second week of December d. Calculate the probability that a selected customer will spend within 30 minutes of the mean amount of time in the third week of December. e. Among 80 customers, determine the probability that at least 35 customers will spend between 45 minutes and 90 minutes on on-line shopping in the first week of December. f. Among 25 customers, determine the probability that no customer will spend at least 2 hours in the second week of December. Question 42. An analysis of the final test scores for Business Statistics reveals the scores follow a normal probability distribution. The mean of the distribution is 72.8 and the standard deviation is The instructor wants to award an A to students whose score is in the highest 15%. What is the diving point for those who earn an A and those earning a B? Question 43. A machine produces computer parts of which 1% are defective. When the machine is tested, a random sample of 15 parts produced by the machine is selected. If a random sample of 15 parts contains at least 2 defectives, the machine is shut down for repairing. Determine the probability that the machine will be shut down for repairing based on the results of the test. A B C D E F G

11 Question 44. A study has shown that 35% of all college textbooks have a price of $140 or higher. It is known that the standard deviation of the prices of all college textbooks is $ Suppose the prices of all the textbooks have a normal distribution. What is the mean price of all the textbooks? Question 45. Sixty percent of the customers of a fast food chain order the Whopper, french fries and a drink. If a random sample of 15 cash register receipts is selected, what is the probability that 10 or more will show that the above three food items were ordered? A B C D E. None of the above 11

12 Question#1 Cannot be computed ANSWERS Question#2 B Question#3 B Question#4 B Question#5 E Question#6 A Question#7 a b Question# Question#9 a b Question# Question# Question#

13 Question# Question# Question#15 0 Question#16 89 Question#17-92 Question# Question#19 none Question#20 none Question#21 a b c.7.532, d Question#22 a. 69, 74, 75 b. 61 Question#23 a b Question#24 b.i ii iii. 19.2=19 calls, 3.82=4calls 13

14 Question#25 a b c d Question#26 a. $ b.1078 Question#27 12 units E (x)=$75.60, 14 units E (X)=$71.60, 15units E(X)=$67.80, select 12 units Question#28 a. Location A E(X)= $95400, Location B E(X)=$83500, Location C E(X)= $79750, select location A b. Location A C.V=68%, Location B C.V=337% Location C C.V=253%, Location A is the lowest risk Question#29 a b c d Question#30 a b c Question#31 a b c d e Question#32 b i ii iii iv c. $34.11 Question#33 a b c d Question#34 a i. $ ii. $ iii. $ iv. $ b. Tire X 14

15 Question#35 $1500 Question#36 23 units Question#37 b i ii Question#38 a b c d Question#39 C Question#40 A Question#41 a b c d e f Question# Question#43 C Question# Question#45 C 15