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Energy Statistics A Guide To Information Sources 1st Edition Sarojini Balachandran - Solutions

81. The mean of a normal probability distribution is 25 with a standard deviation of 8.a. μ ± 1σ of the observations lie between what two values?b. μ ± 2σ of the observations lie between what two values?c. μ ± 3σ of the observations lie between what two values?d. What percentage of the
80. Among cities with a population of more than 250 000, the mean one-way commute time to work is 24.3 minutes providing there are no accidents or inclement weather along the way. A city with a population of 1 million has a mean commute time to work of 38.3 minutes. Assume that the distribution of
79. The distribution of the number of viewers for the American Idol television broadcasts follows the normal distribution with a mean of 29 million and a standard deviation of 5 million. What is the probability that next week’s show will:a. Have between 30 and 34 million viewers?b. Have at least
78. According to the Show Box Office at the Smythe Production Company, the mean cost to run a performance is $3000. Assume that the standard deviation is $410 and that the performance cost follows a normal probability distribution.a. What percentage of the performances cost more than $3100 to
77. The number of cupcakes sold per week at the Coffee Bean Cafe follows the normal probability distribution, with a mean of 150 cupcakes. The standard deviation of this distribution is 5 cupcakes.a. What is the probability that the number sold is between 150 and 154 cupcakes?b. What is the
76. A recent survey reported that the average person consumes six glasses of water per day (250 mL per glass). Assume the standard deviation of water consumption is 378.5 mL per day and the consumption rate follows a normal probability distribution. What is the z-value for a person who drinks 1900
75. DeKorte Tele-Marketing Inc. is considering purchasing a machine that randomly selects and automatically dials telephone numbers. DeKorte Tele-Marketing makes most of its calls during the evening, so calls to business phones are wasted. The manufacturer of the machine claims that its
74. In establishing warranties on high-definition TV (HDTV) sets, the manufacturer wants to set the limits so that few will need repair at manufacturer expense. However, the warranty period must be long enough to make the purchase attractive to the buyer. For a new HDTV, the mean number of months
73. The annual sales of romance novels follow the normal distribution. However, the mean and standard deviation are unknown. Forty percent of the time sales are more than 470 000, and 10% of the time sales are more than 500 000. What are the mean and the standard deviation?
72. The price of shares of the Continental Bank at the end of trading each day for the last year followed the normal distribution. Assume there were 240 trading days in the year. The mean price was $42.00 per share and the standard deviation was $2.25 per share.a. What percentage of the days was
71. Many three-year automobile leases allow up to 100 000 km. If the lease goes beyond this amount, a penalty per kilometre is added to the lease cost. Suppose the distribution of kilometres driven on three-year leases follows the normal distribution. The mean is 85 000 km and the standard
70. The Gravenhurst Enquirer reported that the mean number of hours worked per week by those employed full time is 43.9. The article further indicated that about one-third of those employed full time work less than 40 hours per week.a. Given this information and assuming that number of hours worked
69. The weights of canned hams processed at the Henline Ham Company follow the normal distribution, with a mean of 3.1 kg and a standard deviation of 0.125 kg. The label weight is given as 3 kg.a. What proportion of the hams actually weigh less than the amount claimed on the label?b. The owner,
68. The registrar at Elmwood University (EU) studied the grade point averages (GPAs) of students over many years. Assume the GPA distribution follows a normal distribution with a mean of 3.10 and a standard deviation of 0.30.a. What is the probability that a randomly selected Elmwood student has a
67. The goal at U.S. airports handling international flights is to clear these flights within 45 minutes. Let us interpret this to mean that 95% of the flights are cleared in 45 minutes, so 5% of the flights take longer to clear. Let us also assume that the distribution is approximately normal.a.
65. The Georgetown Traffic Division reported 40% of the high-speed chases involving automobiles result in a minor or major accident. During a month in which 50 high-speed chases occur, what is the probability that 25 or more will result in a minor or major accident? 66. Cruise ships of the Royal
64. It is estimated that 10% of those taking the quantitative methods portion of the certified public accountant (CPA) examination fail that section. Sixty students are taking the examination this Saturday.a. How many would you expect to fail? What is the standard deviation?b. What is the
63. A recent survey reported that 64% of men over the age of 18 consider nutrition a top priority in their lives. Suppose we select a sample of 60 men. What is the likelihood that:a. 32 or more consider nutrition important?b. 44 or more consider nutrition important?c. More than 32 but fewer than
62. The funds dispensed at the automatic teller machine (ATM) at the Queensway site of the Trillium Hospital follows a normal distribution with a mean of $4200 per day and a standard deviation of $720 per day. The machine is programmed to notify the bank if the amount dispensed is very low, less
61. The median age in Canada was 39.5 years (as reported by Statistics Canada). Assume that the distribution of median ages is normally has a standard deviation of 1.5 years.a. What is the probability that the median age is more than 37.0 years?b. What is the probability that the median age is less
60. A recent study shows that 20% of all employees prefer their vacation time during March break. If a company employs 50 people, what is the probability that:a. Fewer than five employees want their vacation during March break?b. More than five employees want their vacation during March break?c.
59. Best Electronics offers a “no hassle” returns policy. The number of items returned per day follows the normal distribution. The mean number of customer returns is 10.3 per day and the standard deviation is 2.25 per day.a. In what percentage of the days eight or fewer customers are returning
58. Fast Service Truck Lines uses the Ford Super 1310 exclusively. Management made a study of the maintenance costs and determined the number of kilometres travelled during the year followed the normal distribution. The mean of the distribution was 96 600 km and the standard deviation 3200 km.a.
57. Management at Gordon Electronics is considering adopting a bonus system to increase production. One suggestion is to pay a bonus on the highest 5% of production on the basis of past experience. Past records indicate weekly production follows the normal distribution. The mean of this
56. According to a government study among adults in the 25- to 34-year age group, the mean amount spent per year on reading and entertainment is $1994. Assume that the distribution of the amounts spent follows the normal distribution with a standard deviation of $450.a. What percentage of the
55. According to a recent survey, the mean number of hours of TV viewing per week is higher among adult women than among men. A recent study showed women spent an average of 34 hours per week watching TV and men 29 hours per week. Assume that the distribution of hours watched follows the normal
54. The annual commissions earned by sales representatives of Machine Products Inc., a manufacturer of light machinery, follow the normal distribution. The mean yearly amount earned is $40 000 and the standard deviation is $5000.a. What percentage of the sales representatives earn more than $42
53. Shaver Manufacturing Inc. offers dental insurance to its employees. A recent study by the human resource director shows the annual cost per employee per year followed the normal distribution, with a mean of $1280 and a standard deviation of $420 per year.a. What is the probability that the
52. A study of long distance phone calls made from the corporate offices of the Pepsi Bottling Group Inc. showed the calls follow the normal distribution. The mean length of time per call was 4.2 minutes and the standard deviation was 0.60 minutes.a. What is the probability the calls lasted between
51. A recent report indicated a typical family of four spends $490 per month on food. Assume the distribution of food expenditures for a family of four follows the normal distribution, with a mean of $490 and a standard deviation of $90.a. What percentage of the families spend more than $30 but
50. The accounting department at Weston Materials Inc., a national manufacturer of unattached garages, reports that it takes two construction workers a mean of 32 hours and a standard deviation of 2 hours to erect the Red Barn model. Assume the assembly times follow the normal distribution.a.
49. The net sales and the number of employees for aluminum fabricators with similar characteristics are organized into frequency distributions. Both are normally distributed. For the net sales, the mean is $180 million and the standard deviation is $25 million. For the number of employees, the mean
48. The average salary of merchandisers is $45 000 per year with a standard deviation of $6000.a. What is the probability that a merchandiser earns more than $55 000 per year?b. What is the probability that a merchandiser earns less than $32 000 per year?c. What is the probability that a
47. A normal population has a mean of 50 and a standard deviation of 7.a. Compute the z-value associated with 45.b. What percentage of the population is between 45 and 63?c. What percentage of the population is less than 55?d. What percentage of the population is more than 40?e. What percentage of
46. Given the following pairs of z-values, find the area under the normal curve between each pair of z-values:a. z = −1.5 and z = 1.75c. z = −2.58 and z = −1.05b. z = 1.23 and z = 2.71d. z = −2.45 and z = −0.79
45. Given the following z-values, find the areas under the normal curve to the left and right of the z-value:a. z = 1.56c. z = −0.78b. z = 1.83d. z = −2.45
44. The time patrons at the Grande Dunes Hotel in the Bahamas spend waiting for an elevator follows a uniform distribution between 0 and 3.5 minutes.a. Show that the area under the curve is 1.00.b. How long does the typical patron wait for elevator service?c. What is the standard deviation of the
43. Many retail stores offer their own credit cards. At the time of the credit application the customer is given a 10% discount on the purchase. The time required for the credit application process follows a uniform distribution with the times ranging from 4 minutes to 10 minutes.a. What is the
42. A tube of Listerine Tartar Control toothpaste contains 4.2 ounces. As people use the toothpaste, the amount remaining in any tube is random. Assume the amount of toothpaste left in the tube follows a uniform distribution. From this information, we can determine the following information about
41. The amount of cola in a 12-ounce can is uniformly distributed between 11.96 ounces and 12.05 ounces.a. What is the mean amount per can?b. What is the standard deviation amount per can?c. What is the probability of selecting a can of cola and finding it has less than 12 ounces?d. What is the
40. Research on new juvenile delinquents put on probation revealed that 38% of them committed another crime.a. What is the probability that of the last 100 new juvenile delinquents put on probation, 30 or more will commit another crime?b. What is the probability that 40 or fewer of the delinquents
39. A study conducted by the nationally known Taurus Health Club revealed that 30% of its new members are significantly overweight. A membership drive in a metropolitan area resulted in 500 new members.a. It has been suggested that the normal approximation to the binomial be used to determine the
38. Shorty’s Muffler advertises that it can install a new muffler in 30 minutes or less. However, the work standards department at corporate headquarters recently conducted a study and found that 20% of the mufflers were not installed in 30 minutes or less. The Maumee branch installed 50 mufflers
37. Dottie’s Tax Service specializes in tax returns for professional clients, such as physicians, dentists, accountants, and lawyers. A recent audit of the returns she prepared indicated that an error was made on 5% of the returns she prepared last year. Assuming this rate continues into this
36. Assume a binomial probability distribution with n = 40 and p = 0.55. Compute the following:a. The mean and standard deviation of the random variable.b. The probability that X is 25 or greater.c. The probability that X is 15 or less.d. The probability that X is between 15 and 25 inclusive.
35. Assume a binomial probability distribution with n = 50 and p = 0.25. Compute the following:a. The mean and standard deviation of the random variable.b. The probability that X is 15 or more.c. The probability that X is 10 or less.
34. The manufacturer of a laser printer reports the mean number of pages a cartridge will print before it needs replacing is 12 200. The distribution of pages printed per cartridge closely follows the normal probability distribution and the standard deviation is 820 pages. The manufacturer wants to
33. The newsstand at the corner of Bloor and Yonge finds that the number of papers sold each day follows a normal probability distribution with a mean of 900 copies and a standard deviation of 150 copies. How many copies should the owner of the newsstand order so that he only runs out of papers on
32. The monthly sales of mufflers follow the normal distribution with a mean of 1200 and a standard deviation of 225. 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?
31. Assume that the mean hourly cost to operate a commercial airplane follows the normal distribution with a mean $2100 per hour and a standard deviation of $250. What is the maximum operating cost for the lowest 3% of the airplanes?
30. Refer to Exercise 24, where the amount requested for home loans followed the normal distribution with a mean of $70 000 and a standard deviation of $20 000.a. What is the minimum amount requested on the largest 3% of loans?b. What is the maximum amount requested on the smallest 10% of loans?
29. The amounts dispensed by a cola machine follow the normal distribution with a mean of 200 mL and a standard deviation of 0.3 mL per cup. How much cola is dispensed in the largest 1% of the cups?
28. A normal distribution has a mean of 80 and a standard deviation of 14. Determine the value above which 80% of the values will occur.
27. A normal distribution has a mean of 50 and a standard deviation of 4. Determine the value below which 95% of the observations will occur.
26. A survey reported that the mean starting salary for college graduates after a three-year program was $33 176. Assume that the distribution of starting salaries follows the normal distribution with a standard deviation of $3500. What percentage of the graduates have starting salaries:a. Between
25. CNAE, an all-news AM station, finds that the distribution of the lengths of time listeners are tuned to the station follows the normal distribution. The mean of the distribution is 15.0 minutes and the standard deviation is 3.5 minutes. What is the probability that a particular listener will
24. The amounts of money requested on home loan applications at Down River Federal Savings follow the normal distribution, with a mean of $70 000 and a standard deviation of $20 000. A loan application is received this morning. What is the probability that:a. The amount requested is $80 000 or
23. A cola-dispensing machine is set to dispense on average 225 millilitres (mL) of cola per cup. The standard deviation is 10 mL. The distribution amounts dispensed follows a normal distribution.a. What is the probability that the machine will dispense between 235 mL and 250 mL of cola?b. What is
22. A normal population has a mean of 80.0 and a standard deviation of 14.0.a. Compute the probability of a value between 75.0 and 90.0.b. Compute the probability of a value 75.0 or less.c. Compute the probability of a value between 55.0 and 70.0.
21. A normal distribution has a mean of 50 and a standard deviation of 4.a. Compute the probability of a value between 44.0 and 55.0.b. Compute the probability of a value greater than 55.0.c. Compute the probability of a value between 52.0 and 55.0.
20. The mean of a normal distribution is 400 kg. The standard deviation is 10 kg.a. What is the area between 415 kg and the mean of 400 kg?b. What is the area between the mean and 395 kg?c. What is the probability of selecting a value at random and discovering that it has a value of less than 395
19. A recent study of the hourly wages of maintenance crews for major airlines showed that the mean hourly salary was $16.50, with a standard deviation of $3.50. If we select a crew member at random, what is the probability the crew member earns:a. Between $16.50 and $20.00 per hour?b. More than
18. A normal population has a mean of 12.2 and a standard deviation of 2.5.a. Compute the z-value associated with 14.3.b. What proportion of the population is between 12.2 and 14.3?c. What proportion of the population is less than 10.0?
17. A normal population has a mean of 20.0 and a standard deviation of 4.0.a. Compute the z-value associated with 25.0.b. What proportion of the population is between 20.0 and 25.0?c. What proportion of the population is less than 18.0?
16. Given the following pairs of z-values, find the area under the normal curve between each pair of z-values.a. z = 1.0 and z = −1.0c. z = 2.83 and z = 1.75b. z = −1.25 and z = −2.0d. z = −2.35 and z = 1.5
15. Given the following z-values, find the areas under the normal curve to the left and right of the z-value.a. z = 1.0c. z = 2.83b. z = −1.25d. z = −2.35
14. A recent article in the Collingwood Sun Times reported that the mean labour cost to repair a heat pump is $90 with a standard deviation of $22. Dawson’s Heating Repairs and Services completed repairs on two heat pumps this morning. The labour cost for the first was $75, and it was $100 for
13. The Kamp family has twins, Rob and Rachel. Both Rob and Rachel graduated from college two years ago, and each is now earning $50 000 per year. Rachel works in the retail industry, where the mean salary for executives with less than five years’ experience is $35 000 with a standard deviation
12. The mean of a normal probability distribution is 350; the standard deviation is 75.a. μ ± 1σ of the observations lie between what two values?b. μ ± 2σ of the observations lie between what two values?c. μ ± 3σ of the observations lie between what two values?
11. The mean of a normal probability distribution is 100; the standard deviation is 15.a. About what percentage of the observations lie between 85 and 115?b. About what percentage of the observations lie between 70 and 130?c. About what percentage of the observations lie between 55 and 145?
10. The mean of a normal probability distribution is 60; the standard deviation is 5.a. About what percentage of the observations lie between 55 and 65?b. About what percentage of the observations lie between 50 and 70?c. About what percentage of the observations lie between 45 and 75?
9. The mean of a normal probability distribution is 500; the standard deviation is 10.a. About 68% of the observations lie between what two values?b. About 95% of the observations lie between what two values?c. Nearly all of the observations lie between what two values?
8. List the major characteristics of a normal probability distribution.
7. Explain what is meant by this statement: “There is not just one normal probability distribution but a ‘family’ of them.”
6. Customers experiencing technical difficulty with their Internet cable hookup may call an 800 number for technical support. It takes the technician between 30 seconds to 10 minutes to resolve the problem. The distribution of this support time follows the uniform distribution.a. What are the
5. The waiting time, in minutes, for service at the Tim Hortons at the front entrance of the college, follows a uniform distribution between 0.5 and 8.0 minutes.a. What are the values for a and b?b. What is the mean amount of waiting time in minutes? What is the standard deviation?c. What is the
4. According to an insurance survey, a family of four spends between $400 and $3800 per year on all types of insurance. Suppose the money spent is uniformly distributed between these amounts.a. What is the mean amount spent on insurance?b. What is the standard deviation of the amount spent?c. If we
3. The closing price of Schnur Sporting Goods, Inc., common stock is uniformly distributed between $20 and $30 per share. What is the probability that the stock price will be:a. More than $27?b. Less than or equal to $24?
2. A uniform distribution is defined over the interval from 2 to 5.a. What are the values for a and b?b. What is the mean of this uniform distribution?c. What is the standard deviation?d. Show that the total area is 1.00.e. Find the probability of a value more than 2.6.f. Find the probability of a
1. A uniform distribution is defined over the interval from 6 to 10.a. What are the values for a and b?b. What is the mean of this uniform distribution?c. What is the standard deviation?d. Show that the total area is 1.00.e. Find the probability of a value more than 7.f. Find the probability of a
6. MegaStat steps to create the Poisson probability distribution for the lost luggage example are as follows:a. Select MegaStat, Probability, and Discrete Probability Distributions.b. Select the Poisson tab. Enter 0.3 for mu, mean rate of occurrence. Leave maximum x value (optional) blank. To add a
5. Excel steps to create the Poisson probability distribution for the lost luggage example are as follows:a. On a blank Excel worksheet enter the word Success in cell A1 and the word Probability in B1. In cells A2 through A7, enter the integers 0 to 5 (for 0 to 5 lost bags). Click B2 as the active
4. MegaStat steps to create the hypergeometric probability distribution for the PlayTime Toys example are as follows:a. Select MegaStat, Probability, and Discrete Probability Distributions.b. Select the Hypergeometric tab. Enter 50 for N, population size, 40 for s, number of possible occurrences,
3. Excel steps to create the hypergeometric probability distribution for the PlayTime Toys example are as follows:a. On a blank Excel worksheet enter the word Success in cell A1 and the word Probability in B1. In cells A2:A7, enter the integers 0 to 5. Click B2 as the active cell.b. Select Insert
2. Excel steps to create the binomial probability distribution for the number of dropped calls example are as follows:a. In a blank Excel worksheet, enter the word Number of Dropped Calls in cell A1 and the word Probability in B1. In cells A2 through A8, enter the integers 0 to 6. Click B2 as the
1. MegaStat steps to create the binomial probability distribution for the worm gears example are as follows:a. Select MegaStat, Probability, and Discrete Probability Distributions.b. Select the Binomial tab. Enter 6 for n_number of trials and 0.05 for p_probability of occurrence. To display a
3. A data entry clerk studied the number of errors found on expense forms. The data are summarized in the following table: Errors Found Percentage 1 20 2 50 3 20 4 10a. What is the mean number of errors found?b. What is the variance of the number of errors found?
2. Under certain conditions, the Canada Revenue Agency (CRA) will compute the amount of refund that is due to a taxpayer. Suppose that the Vancouver office of the CRA completes an average of three of this type of return per hour.a. Which probability distribution applies to this situation?b. What is
1. An auditor suggests that 15% of tax returns where the gross income is more than $1 000 000 will be subject to computer audit. For a particular year a certified general accountant (CGA) completed 16 returns where the adjusted gross income was more than $1 000 000.a. Which probability model does
10. The mean number of work-related accidents per month in a manufacturing plant is 1.70. What is the probability that there will be no work-related accidents in a particular month?
9. Suppose that 5% of patients who take a certain drug suffer undesirable side effects. If we select 10 patients currently taking the drug, what is the probability that exactly two suffer undesirable side effects?
8. The Poisson distribution is a limiting case of the probability distribution when n is large and π is small.
7. In a Poisson experiment, the mean and the variance are .
6. Under what conditions will the probability of a success change from trial to trial in a binomial experiment? .
5. How many outcomes are there in a particular binomial trial? .
4. The expected value of a probability distribution is also called the .
3. In a discrete probability distribution, the sum of the possible probabilities is always equal to .
2. The essential difference between a discrete random variable and a discrete probability distribution is a discrete probability distribution includes the .
1. A listing of the possible outcomes of an experiment and the probability associated with each outcome is called a .
80. Refer to the real estate data for the Saskatoon area (on Connect), which include information on home listings.a. Create a probability distribution for the number of full bathrooms. Compute the mean and standard deviation of this distribution.b. Create a probability distribution for the number

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