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Energy Statistics A Guide To Information Sources 1st Edition Sarojini Balachandran - Solutions
79. Refer to the real estate data for the Orleans area (on Connect), which include information on home listings for February 2014.a. Create a probability distribution for the number of bedrooms. Compute the mean and standard deviation of this distribution.b. Create a probability distribution for
78. The payouts for the U.S. Powerball lottery and their corresponding odds and probabilities of occurrence are shown below. The price of a ticket is $1.00. Find the mean and standard deviation of the payout. (Hint: be sure to include the cost of the ticket and its corresponding probability.)
77. A recent CBS News survey reported that 67% of adults felt the U.S. Treasury should continue making pennies. Suppose that we select a sample of 15 adults.a. How many of the 15 would we expect to indicate that the Treasury should continue making pennies? What is the standard deviation?b. What is
76. Suppose the National Hurricane Centre forecasts that hurricanes will hit the strike area with a 0.95 probability.a. What is the probability that 10 hurricanes reach landfall in the strike area?b. What is the probability at least one of 10 hurricanes reaches land outside the strike area?
75. Recent difficult economic times have caused an increase in the foreclosure rate of home mortgages. Statistics from the Penn Bank and Trust Company show their monthly foreclosure rate is now one loan out of every 136 loans. Last month the bank approved 300 loans.a. How many foreclosures would
74. Unilever Inc. recently developed a new body wash with a scent of ginger. Their research indicates that 30% of men like the new scent. To further investigate, Unilever’s marketing research group randomly selected 15 people and asked them whether they liked the scent. What is the probability
73. Acceptance sampling is a statistical method used to monitor the quality of purchased parts and components. To ensure the quality of incoming parts, a purchaser or manufacturer normally samples 20 parts and allows one defect.a. What is the likelihood of accepting a lot that is 1% defective?b. If
72. In the past, schools in northern Manitoba have closed an average of three days each year due to weather conditions. What is the probability that schools in that area will close for four days next year?
71. It is asserted that 80% of the cars approaching an exit point on the 407 ETR (Express Toll Route) are equipped with an ETR transponder. Find the probability that in a sample of six cars:a. All six will have the transponder.b. At least three will have the transponder.c. None will have a
70. Simone has a quiz in class today. The quiz will consist of 10 multiple-choice questions, each with four possible answers. Simone has not had time to review the material or to do the practice questions and figures that she will have to guess the correct answers. What is the probability that
69. A recent study revealed that 40% of women in the St. John’s area who work full time also volunteer in the community. Suppose we randomly select eight women in the St. John’s area.a. What is the probability that exactly three of the women volunteer in the community?b. What is the
68. Number of Big Screen TVs Sold X Number of Days 0 4 1 15 2 5 3 3 4 2 5 1 Total 30a. Construct a probability distribution for X = number of big screen TVs sold.b. What is the expected number of big screen TVs sold per month? Interpret this value.c. The price of a big screen TV is on average $3575
67. During the second round of the 1989 U.S. Open golf tournament, four golfers scored a hole-in-one on the sixth hole. The odds of a professional golfer making a hole-in-one are estimated to be 3708 to 1, so the probability is 1/3709. There were 155 golfers participating in the second round that
66. According to the “January theory,” if the stock market is up for the month of January, it will be up for the year. If it is down in January, it will be down for the year. According to an article in The Wall Street Journal, this theory has held for 29 out of the last 34 years. Suppose there
65. The National Aeronautics and Space Administration (NASA) has experienced two disasters. The Challenger exploded over the Atlantic Ocean in 1986, and the Columbia exploded over east Texas in 2003. There have been a total of 123 space missions. Assume that failures continue to occur at the same
64. New Process Inc., a large mail-order supplier of women’s fashions, advertises same-day service on every order. Recently, the movement of orders has not gone as planned, and there were a large number of complaints. Bud Owens, director of customer service, has completely redone the method of
63. Recent crime reports indicate that 18.4 motor vehicle thefts occur every hour in Canada. Assume that the distribution of thefts per hour can be approximated by a Poisson probability distribution.a. Calculate the probability exactly four thefts occur in an hour.b. What is the probability there
62. An internal study at Lahey Electronics, a large software development company, revealed the mean time for an internal email message to arrive at its destination was two seconds. Further, the distribution of the arrival times followed a Poisson distribution.a. What is the probability a message
61. A study of the checkout lines at the Safeway Supermarket revealed that between 4 p.m. and 7 p.m. on weekdays, there is an average of four customers waiting in line. What is the probability that you visit Safeway today during this period and find:a. No customers are waiting?b. Four customers
59. The sales of Lexus automobiles in the Calgary area follow a Poisson distribution with a mean of three per day.a. What is the probability that no Lexus is sold on a particular day?b. What is the probability that for five consecutive days at least one Lexus is sold? 60. Suppose 1.5% of the
58. A manufacturer of computer chips claims that the probability of a defective chip is 0.002. The manufacturer sells chips in batches of 1000 to major computer companies.a. How many defective chips would you expect in a batch?b. What is the probability that none of the chips are defective in a
57. A recent study conducted by Penn, Shone, and Borland, on behalf of LastMinute.com, revealed that 52% of business travellers plan their trips less than 2 weeks before departure. The study is to be replicated in the London area with a sample of 12 frequent business travellers.a. Develop a
56. Dr. Richmond, a psychologist, is studying the daytime television viewing habits of college students. She believes 45% of college students watch soap operas during the afternoon. To further investigate, she randomly selects a sample of 10.a. Develop a probability distribution for the number of
55. Recent statistics suggest that 15% of those who visit a retail site on the World Wide Web make a purchase. A retailer wished to verify this claim. To do so, she selected a sample of 16 “hits” to her site and found that four had actually made a purchase.a. What is the likelihood of exactly
54. The Bank of Hudson Bay reports that 7% of its credit card holders will default at some time in their life. The Moose Factory branch just mailed out 12 new cards today.a. How many of these new cardholders would you expect to default? What is the standard deviation?b. What is the likelihood that
53. A study reported that 7.5% of the workforce has a drug problem. A drug enforcement official wished to investigate this statement. In his sample of 20 employed workers:a. How many would you expect to have a drug problem? What is the standard deviation?b. What is the likelihood that none of the
52. Tire and Auto Supply is considering a 2-for-1 stock split. Before the transaction is finalized, at least two-thirds of the 1200 company stockholders must approve the proposal. To evaluate the likelihood the proposal will be approved, the director of finance randomly selected a sample of 18
51. An auditor for an insurance company in Alberta reports 40% of the policyholders 55 years or older submit a claim during the year. Fifteen policyholders are randomly selected for company records.a. How many of the policyholders would you expect to have filed a claim within the last year?b. What
50. Three tables listed below show random variables and their probabilities. However, only one of these is actually a probability distribution. x P(x) x P(x) x P(x) 25 0.1 25 −0.6 25 0.5 50 0.7 50 0.2 50 0.3 75 0.2 75 0.1 75 0.1 100 0.4 100 0.1 100 0.1a. Which of the above tables is a probability
49. Which of these variables are discrete and which are continuous random variables?a. The number of new sales associates hired for the Christmas season.b. The time between buses from the airport to downtown.c. The number of students registered in second year accounting.d. The number of cups of
48. In a recent survey, 35% indicated chocolate was their favorite flavour of ice cream. Suppose that we select a sample of 10 people and ask them to name their favourite flavour of ice cream.a. How many of those in the sample would you expect to name chocolate?b. What is the probability exactly
47. Croissant Bakery Inc. offers specially decorated cakes for birthdays, weddings, and other occasions. It also has regular cakes available in its display case. The following table gives the total number of cakes sold per day and the corresponding probability. Compute the mean, variance, and
46. In the game of heads or tails, if two coins are tossed, you win $0.75 if you throw two heads, win $0.50 if you throw a head and a tail, and lose $1.00 if you throw two tails. What are the expected winnings of this game?
45. The vice-president of human resources at Lowes Inc. is studying the number of on-the-job accidents over a period of one month. He developed the following probability distribution. Compute the mean, variance, and standard deviation of the number of accidents in a month. Number of Accidents
44. An investment will be worth $1000, $2000, or $5000 at the end of the year. The probabilities of these values are 0.25, 0.60, and 0.15, respectively. Determine the mean and the variance of the worth of the investment.
43. Samson Apartments has a large number of units available to rent each month. A concern of management is the number of vacant apartments each month. A recent study revealed the percentage of the time that a given number of apartments are vacant. Compute the mean and the standard deviation of the
42. Under what conditions will the binomial and the Poisson distributions give roughly the same results?
41. What are the requirements for the binomial distribution?
40. For each of the following, indicate whether the random variable is discrete or continuous.a. The length of time to get a haircut.b. The number of cars a jogger passes each morning while running.c. The number of hits for a team in a high school girls’ softball game.d. The number of patients
39. What is the difference between a random variable and a probability distribution?
38. Textbook authors and publishers work very hard to minimize the number of errors in a text. However, some errors are unavoidable. Ms. Kimberley Veevers, statistics editor, reports that the mean number of errors per chapter is 0.8. What is the probability that there are less than two errors in a
37. It is estimated that 0.5% of the callers to the billing department of a local telephone company will receive a busy signal. What is the probability that of today’s 1200 callers at least five received a busy signal?
36. Automobiles frequently arrive at the Bronte exit of the Queen Elizabeth Way at the rate of two per minute. The distribution of arrivals approximates a Poisson distribution.a. What is the probability that no automobiles arrive in a particular minute?b. What is the probability that at least one
35. Ms. Bergen is a loan officer at a trust company. On the basis of her years of experience, she estimates that the probability is 0.025 that an applicant will not be able to repay his or her installment loan. Last month she made 40 loans.a. What is the probability that three loans will be
34. In a Poisson distribution, μ = 4.a. What is the probability that x = 2?b. What is the probability that x ≤ 2?c. What is the probability that x > 2?
33. In a Poisson distribution, μ = 0.4.a. What is the probability that x = 0?b. What is the probability that x > 0?
32. Professor Jon Hammer has a pool of 15 multiple-choice questions regarding probability distributions. Four of these questions involve the hypergeometric distribution. What is the probability at least one of these hypergeometric questions will appear on the five-question quiz on Monday?
31. Keith’s Florists has 15 delivery trucks used mainly to deliver flowers and flower arrangements. Of these 15 trucks, six have brake problems. A sample of five trucks is randomly selected. What is the probability that two of those tested have defective brakes?
30. The computer systems department has eight faculty members, six of whom are tenured. Dr. Vonder, the chairman, wants to establish a committee of three department faculty members to review the curriculum. If she selects the committee at random:a. What is the probability all members of the
29. Kolzak Appliance Outlet just received a shipment of 10 TV sets. Shortly after they were received, the manufacturer called to report that he had inadvertently shipped three defective sets. Ms. Kolzak, the owner of the outlet, decided to test two of the 10 sets she received. What is the
28. A population consists of 15 items, 10 of which are acceptable. In a sample of four items, what is the probability that exactly three are acceptable?
27. A population consists of 10 items, six of which are defective. In a sample of three items, what is the probability that exactly two are defective?
26. Steele Electronics Inc. sells expensive brands of stereo equipment in several shopping malls. The marketing research department of Steele reports that 30% of the customers entering the store that indicate they are browsing will, in the end, make a purchase. Let the last 20 customers who enter
25. The speed with which utility companies can resolve problems is very important. The Georgetown Telephone Company (GTC), reports that it can resolve customer problems the same day they are reported in 70% of the cases. Suppose that the 15 cases reported today are representative of all
24. A manufacturer of window frames knows from long experience that 5% of the production will have some type of minor defect that will require an adjustment. What is the probability that in a sample of 20 window frames:a. None will need adjustment?b. At least one will need adjustment?c. More than
23. In a recent study, 90% of homes in Canada were found to have large-screen TVs. In a sample of nine homes, what is the probability that:a. All nine have large-screen TVs?b. Less than five have large-screen TVs?c. More than five have large-screen TVs?d. At least seven homes have large-screen TVs?
22. In a binomial distribution, n = 12 and p = 0.60. Find the following probabilities:a. x = 5.b. x ≤ 5.c. x ≥ 6.
21. In a binomial distribution, n = 8 and p = 0.30. Find the probabilities of the following events:a. x = 2.b. x ≤ 2 (the probability that x is equal to or less than 2).c. x ≥ 3 (the probability that x is equal to or greater than 3).
20. It is reported that 16% of American households use a cell phone exclusively for their telephone service. In a sample of eight households, find the probability that:a. None uses a cell phone as the exclusive service.b. At least one uses the cell phone exclusively.c. At least five use the cell
19. A recent survey of first-year college students found that 23% choose accounting as their major. Suppose that we select a sample of 15 first-year students.a. What is the probability that two chose accounting?b. What is the probability that five chose accounting?c. How many of the 15 would you
18. A telemarketer makes six phone calls per hour and is able to make a sale on 30% of these contacts. During the next two hours, find:a. The probability of making exactly four sales.b. The probability of making no sales.c. The probability of making exactly two sales.d. The mean number of sales in
17. Industry standards suggest that 10% of new vehicles require warranty service within the first year. Jones Nissan, sold 12 Nissans yesterday.a. What is the probability that none of these vehicles requires warranty service?b. What is the probability exactly one of these vehicles requires warranty
16. A local courier service reports that 95% of bulk parcels within the same city are delivered within two days. Six parcels are randomly sent to different locations.a. What is the probability that all six arrive within two days?b. What is the probability that exactly five arrive within two days?c.
15. An investment firm’s survey found 30% of individual investors have used a discount broker. In a random sample of nine individuals, what is the probability that:a. Exactly two of the sampled individuals have used a discount broker?b. Exactly four of them have used a discount broker?c. None of
14. Assume a binomial distribution where n = 5 and p = 0.30.a. Refer to Appendix B.3, and list the probabilities for values of x from 0 to 5.b. Determine the mean and standard deviation of the distribution from the general definitions given in formulas (5–1) and (5–2).
13. Assume a binomial distribution where n = 3 and p = 0.60.a. Refer to Appendix B.3, and list the probabilities for values of x from 0 to 3.b. Determine the mean and standard deviation of the distribution from the general definitions given in formulas (5–1) and (5–2).
12. In a binomial situation, n = 5 and p = 0.40. Determine the probabilities of the following events using the binomial formula:a. x = 1b. x = 2c. x > 2d. x ≤ 4
11. In a binomial situation, n = 4 and p = 0.25. Determine the probabilities of the following events using the binomial formula:a. x = 2b. x = 3c. x ≥ 2d. x < 3
10. The parking authority in downtown Halifax reported the following information for a sample of 250 customers on the number of hours cars are parked and the amount they are charged: Number of Amount Hours Frequency Charged 1 20 $3 2 38 6 3 53 9 4 45 12 5 40 14 6 13 16 7 5 18 8 36 20a. Convert the
9. Belk Department Store is having a special sale this weekend. Customers charging purchases of more than $50 to their Belk credit card will be given a special Belk Lottery card. The customer will scratch off the card, which will indicate the amount to be taken off the total amount of the purchase.
8. You are asked to match three songs with the performers who made those songs famous. If you guess, the probability distribution for the number of correct matches is: Probability 0.333 0.500 0.000 0.167 Number correct 0 1 2 3 What is the probability you will get:a. Exactly one correct?b. At least
7. The following table lists the probability distribution for cash prizes in a lottery conducted at Lawson’s Department Store: Prize ($) Probability $0 0.45 10 0.30 100 0.20 500 0.05 If you buy a single ticket, what is the probability that you will win:a. Exactly $100?b. At least $10?c. No more
6. The director of admissions at Kinzua University in Nova Scotia estimated the distribution of student admissions for the fall semester on the basis of past experience. What is the expected number of admissions for the fall semester? Compute the variance and the standard deviation. Admissions
5. The information below is the number of daily emergency assists made to skiers by the volunteer ski team at Alpine Ski Lodge for the last 50 days. To explain, there were 22 days on which there were 2 emergency assists, and 9 days on which there were 3 emergency assists. Number of Calls Frequency
4. Which of these variables are discrete variables, and which are continuous random variables?a. The number of new accounts established by a salesperson in a year.b. The time between customer arrivals to a bank automatic teller machine (ATM).c. The number of customers in Big Nick’s barber shop.d.
3. Three tables listed below show random variables and their probabilities. However, only one of these is actually a probability distribution. x P(x) 5 0.1 10 0.2 15 0.3 20 0.4 x P(x) 5 0.5 10 0.3 15 -0.2 20 0.4 x P(x) 5 0.3 10 0.3 15 0.2 20 0.4a. Which of the above tables is a probability
2. Compute the mean and variance of the following discrete probability distribution: x P(x) 2 0.5 8 0.3 10 0.2
1. Compute the mean and variance of the following discrete probability distribution: x P(x) 0 0.2 1 0.4 2 0.3 3 0.1
4. MegaStat commands to find the number of combinations the Grand movie theatre example are:a. Select MegaStat, Probability, Counting Rules, and select the Combinations tab.b. Enter 7 in the first box (for n) and 3 in the second box (for r).c. Click the Preview box to see the answer, or click OK
3. MegaStat commands to find the number of permutations for the Betts Machine Shop Inc. example are:a. Select MegaStat, Probability, Counting Rules, and select the Permutations tab.b. Enter 8 in the first box (for n) and 3 in the second box (for r).c. Click the Preview box to see the answer and/or
2. Excel steps to determine the number of combinations for the Grand movie theatre example are:a. Select Insert Function. From the Or select a category list, select Math & Trig.b. In the Select a function list, click COMBIN. Click OK.c. Enter 7 for Number and 3 for Number_chosen. The answer of 35
1. Excel steps to determine the number of permutations for the Betts Machine Shop Inc. example are:a. Select Insert Function. From the Or select a category list, select Statistical.b. In the Select a function list, click PERMUT. Click OK.c. Enter 8 for Number and 3 for Number_chosen. The answer of
3. Fred works in a tax office with four other certified general accountants (CGAs). There are five parking spots beside the office. If they all drive to work, how many different ways can the cars belonging to the CGAs be arranged in the five spots? .
2. Fred exercises regularly. He jogs 30% of the time, rides a bike 20% of the time, and does both 12% of the time. What is the probability that on a typical day he does at least one of these two types of exercise?
1. Fred Friendly, CGA, has 20 tax returns to prepare before the April 30 deadline. It is late at night, so he decides to do two more before going home. In his stack of accounts, 12 are for individuals, 5 are for businesses, and 3 are for charitable organizations. If he selects the two returns at
11. A probability that measures the likelihood two or more events will happen concurrently is called a . 12. The special rule of multiplication requires that two events A and B are
10. The is used to determine the probability of an event occurring by subtracting the probability of the event not occurring from 1.
9. If two events A and B are , the special rule of addition states that the probability of one or the other events occurring equals the sum of their probabilities.
8. If an experiment has a set of events that includes every possible outcome, then the set of events is described as .
7. If several events are described as , then the occurrence of one event means that none of the other events can occur at the same time.
6. Using the viewpoint, the probability of an event happening is computed by dividing the number of favourable outcomes by the number of possible outcomes.
5. Using the viewpoint, an individual evaluates the available opinions and information and then estimates or assigns the probability.
4. Using the viewpoint, the probability of an event happening is the fraction of the time similar events happened in the past.
3. An is a collection of one or more outcomes of an experiment.
2. An is a process that leads to the occurrence of one and only one of several possible observations.
1. A is a value between 0 and 1, inclusive, describing the relative chance or likelihood an event will occur.
112. Refer to real estate data for the Saskatoon area (on Connect), which include information on list prices, type, number of full and half bathrooms, number of bedrooms, and total square feet. Sort the data into a table by list price (class widths of $500 000) and the square footage (class widths
111. Refer to real estate data for the Saskatoon area (on Connect), which include information on list prices, type, number of full and half bathrooms, number of bedrooms, and total square feet. Sort the data into a table by list price (class widths of $500 000) and the number of bedrooms. Compute
110. Refer to real estate data for the Saskatoon area (on Connect), which include information on list prices, type, number of full and half bathrooms, number of bedrooms, and total square feet. Sort the data into a table by type and list price (in class widths of $500 000), and compute the
109. Refer to real estate data from the Saskatoon area (on Connect) which include information on list prices, type, number of full and half bathrooms, number of bedrooms and total square feet.a. What is the probability that a listing is less than $200 000?b. What is the probability that a listing
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