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mathematics
statistics

Elementary Statistics 3rd Canadian Edition Mario F. Triola - Solutions

Suppose that a gas pipeline averages 1 blemish per 40 km. Find the following probabilities for a section of the pipeline. Less than 80 km between successive blemishes if there is at least 35 km between successive blemishes
Suppose that when a grocery store has 3 cashiers working during its afternoon rush period, a customer waits 8 minutes on average to be served. If there are 2 cashiers working, what is the probability a customer waits more than 15 minutes in total if the customer has already been waiting 10 minutes?
Suppose that when a grocery store has 3 cashiers working during its afternoon rush period, a customer waits 8 minutes on average to be served. If there are 5 cashiers, what is the probability a customer will wait less than 5 minutes?
Suppose that when a call centre has 25 CSRs, a customer waits 1.5 minutes on average for each person ahead in the queue. Which has the greater probability: (a) waiting more than 20 minutes when there are 25 CSRs and 7 people ahead in the queue or (b) waiting more than 20 minutes when there are 30
Suppose that when a call centre has 25 CSRs, a customer waits 1.5 minutes on average for each person ahead in the queue. Suppose there are 10 CSRs and 18 people ahead in the queue. If you have been waiting 40 minutes already, does it seem realistic that you will wait no more than one hour in total
Assume that college statistics students have normally distributed heights with a mean of 68.0 in. and a standard deviation of 4.36 in. (based on Data Set 8 in Appendix B). You plan to sell sweat suits in the college bookstore. To minimize start-up costs, you will not stock sweat suits for the
The Chemco Company manufactures car tires that last distances that are normally distributed with a mean of 57,300 km and a standard deviation of 6875 km. a. If a tire is randomly selected, what is the probability that it lasts more than 48,000 km? b. If 40 tires are randomly selected, what is the
Assume that the print time for a photocopier to copy 20 pages is uniformly distributed between 20.2 and 21.6 seconds. Find the following probabilities for 20 pages: Print time is less than 21 seconds.
Assume that the print time for a photocopier to copy 20 pages is uniformly distributed between 20.2 and 21.6 seconds. Find the following probabilities for 20 pages: Print time is more than 20.5 seconds.
Assume that the print time for a photocopier to copy 20 pages is uniformly distributed between 20.2 and 21.6 seconds. Find the following probabilities for 20 pages: Print time is between 20.4 and 21.0 seconds.
Suppose that when a company has 5 customer service reps (CSRs) in its call centre at any given time, they collectively serve 40 customers per hour on average. If there are 5 CSRs, what is the probability that a customer waits more than 2 minutes to speak to a CSR?
Suppose that when a company has 5 customer service reps (CSRs) in its call centre at any given time, they collectively serve 40 customers per hour on average. If there are 5 CSRs, what is the probability that a customer waits more than 2 minutes in total after already waiting 30 seconds?
Suppose that when a company has 5 customer service reps (CSRs) in its call centre at any given time, they collectively serve 40 customers per hour on average. Suppose there are only 4 CSRs instead of 5. What is the probability that a customer waits more than 2 minutes?
Suppose that when a company has 5 customer service reps (CSRs) in its call centre at any given time, they collectively serve 40 customers per hour on average. If there are 8 CSRs, what is the probability that a customer will speak to a CSR within 2 minutes after already waiting 30 seconds?
Assume that college statistics students have normally distributed heights with a mean of 68.0 in. and a standard deviation of 4.36 in. (based on Data Set 8 in Appendix B). The Beanstalk Club is a social organization for tall people. Students are eligible for membership if they are at least 74 in.
Assume that college statistics students have normally distributed heights with a mean of 68.0 in. and a standard deviation of 4.36 in. (based on Data Set 8 in Appendix B). The tallest player on the varsity basketball team is 80 in. tall. The shortest player is 69 in. tall. What percentage of
Assume that college statistics students have normally distributed heights with a mean of 68.0 in. and a standard deviation of 4.36 in. (based on Data Set 8 in Appendix B). If 45 students are randomly selected, what is the probability that their mean height is between 67.0 in. and 71.0 in.?
In a survey, the Canadian Automobile Association (CAA) found that 58% of its members paid cash for their vehicles. Estimate the probability that when 500 CAA members are randomly selected, the number who paid cash is between 250 and 290 inclusive.
The Gleason Supermarket uses a scale to weigh produce, and errors are normally distributed with a mean of 0 oz and a standard deviation of 1 oz (The errors can be positive or negative.) One item is randomly selected and weighed. Find the probability that the error is a. Between 0 and 1.25 oz b.
Scores on the biology portion of the Medical College Admissions Test are normally distributed with a mean of 8.0 and a standard deviation of 2.6. Among 600 individuals taking this test, how many are expected to score between 6.0 and 7.0?
On the Graduate Record Exam in economics, scores are normally distributed with a mean of 615 and a standard deviation of 107. If a college admissions office requires scores above the 70th percentile, find the cutoff point.
According to the National Hockey League Official Guide and Record Book 1998-1999, the top goalie in the season let only 6.8% of the shots fired at him into the net for a goal. In a season in which 1739 shots are fired at the goalie, estimate the probability that more than 120 shots will result in a
According to data from Statistics Canada, Chinese is the mother tongue of 8.1% of Toronto residents. a. If 3 Toronto residents are randomly selected, find the probability that they all have Chinese as their mother tongue. b. If 3 Toronto residents are randomly selected, find the probability that at
The sample scores given below are times (in milliseconds) it took the author's disk drive to make one revolution. The times were recorded by a diagnostic software program.a. Find the mean of the times in this sample.b. Find the median of the times in this sample.c. Find the mode of the times in
Find the critical value zα/2 that corresponds to the given degree of confidence. 99 %
A sample consists of 75 TV sets purchased several years ago. The replacement times of those TV sets have a mean of 8.2 years and a standard deviation of 1.1 years (based on data from "Getting Things Fixed," Consumer Reports). Construct a 90% confidence interval for the mean replacement time of all
A Lyman Electronic Digital Caliper was used to accurately measure the lengths of 40 Triton Quik-Shok 380 ACP 90 grain cartridges (bullets). The results (in millimeters) are listed below. The cartridges are supposed to have a mean length of 0.950 mm and they must be between 0.945 mm long and 0.955
An economist is studying the annual revenues of top Canadian companies. The results of a random sample of such revenues (in billions of dollars) are listed below (based on Data Set 6 in Appendix B). Construct a 95% confidence interval estimate of the mean annual revenue for "Top 100" companies.
The standard IQ test is designed so that the mean is 100 and the standard deviation is 15 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of statistics students. We want to be 98% confident that our sample mean is within 1.5 IQ points of the true
The McLean Vending Machine Company must adjust its machines to accept only coins with specified weights. We will obtain a sample of quarters and weigh them to determine the mean. How many quarters must we randomly select and weigh if we want to be 99% confident that the sample mean is within 0.025
If we refer to the weights (in grams) of quarters listed in Data Set 13 in Appendix B, we will find 50 weights with a mean of 5.622 g and a standard deviation of 0.068 g. Based on this random sample of quarters in circulation, construct a 98% confidence interval estimate of the population mean of
Data Set 18 in Appendix B gives the body temperatures in degrees Celsius of adults accepted for voluntary surgery. For that sample, the mean is 36.39°C and the standard deviation is 0.62°C. Construct a 99% confidence interval for the mean body temperature of the general population and interpret
A psychologist has developed a new test of spatial perception, and she wants to estimate the mean score achieved by male pilots. How many people must she test if she wants the sample mean to be in error by no more than 2.0 points, with 95% confidence? An earlier study suggests that σ = 21.2.
To plan for the proper handling of household garbage, the city of Fredericton must estimate the mean weight of garbage discarded by households in one week. Find the sample size necessary to estimate that mean if you want to be 96% confident that the sample mean is within 2 lb of the true population
A large sample of data (n = 335) from a Calgary observatory produced a mean daily counting rate for cosmic rays of 3465.46, and a standard deviation of 127.72. Use these sample data to find the 90% confidence interval for the mean of the daily counting rates. Suppose a scientist claims that the
Find the critical value zα/2 that corresponds to the given degree of confidence. 94 %
A random sample of 250 Ontario households using natural gas heating shows that the mean monthly consumption of natural gas is 107.73 cu. ft., with a standard deviation of 13.94 cu. ft. Use these statistics to construct a 94% confidence interval for the mean monthly consumption for the population of
Nielsen Media Research wants to estimate the mean amount of time (in hours) that full-time college students spend watching television each weekday. Find the sample size necessary to estimate that mean with a 0.25 h (or 15 min) margin of error. Assume that a 96% degree of confidence is desired. Also
In deciding whether to attend university, many students are influenced by the increased earnings potential that a university degree is likely to create. A recent census study by Statistics Canada shows that the mean annual income of high-school graduates is $22,846, whereas the mean annual income
You have just been hired by the Stampeder Marketing Company to conduct a survey to estimate the mean amount of money spent by movie patrons (per movie) in Alberta. First use the range rule of thumb to make a rough estimate of the standard deviation of the amounts spent. It is reasonable to assume
Estimate the minimum and maximum ages for typical textbooks currently used in college courses, then use the range rule of thumb to estimate the standard deviation. Next, find the size of the sample required to estimate the mean age (in years) of textbooks currently used in college courses. Assume a
Refer to Data Set 1 in Appendix B for the 62 weights (in pounds) of paper discarded by households. Using that sample, construct a 92% confidence interval estimate of the mean weight of paper discarded by all households.
Refer to Data Set 1 in Appendix B and construct a 92% confidence interval for the mean weight in pounds of discarded plastic goods per household for one week. Compare these results with your solution to Exercise 25, and interpret. Which is more of an ecological problem: discarded paper or discarded
Refer to Data Set 11 in Appendix B and construct a 97% confidence interval for the mean weight of brown M&M plain candies. Can the methods of this section be used to construct a 97% confidence interval for the mean weight of blue M&M plain candies? Why or why not?
Refer to Data Set 8 in Appendix B and construct a 98% confidence interval for the mean value of coins in possession of statistics students. Is there reason to believe that this value is different from the mean value of coins in possession of people randomly selected from the general population of
In Formula 6-1 we assume that the population is infinite, that we are sampling with replacement, or that the population is very large. If we have a relatively small population such that n > 0.05N, and sample without replacement, we should modify £ to include a finite population correction
Find the critical value zα/2 that corresponds to the given degree of confidence. 98 %
Test the effect of an outlier as follows: Use the sample data in Table 6-1 to find a 95% confidence interval estimate of the population mean, but change the first entry from 36.4 to 364. Nobody can really have that high a body temperature, but such an error can easily occur when a decimal point is
In many of the preceding examples, confidence intervals are used toward the ultimate goal of estimating the value of a population parameter. Confidence intervals can also be used as a data-exploration tool, for describing and comparing data sets. Consider the following descriptive statistics, taken
A 95% confidence interval for the lives (in minutes) of Kodak AA batteries is 430 < µ < 470. (See Program 1 of Against All Odds: Inside Statistics.) Assume that this result is based on a sample of size 100. a. Construct the 99% confidence interval. b. What is the value of the sample mean? c. What
Find the critical value zα/2 that corresponds to the given degree of confidence. 92 %
Use the given degree of confidence and sample data to find(a) The margin of error(b) The confidence interval for the population mean µ.Heights of female students: 95% confidence; n = 50, = 64.2 in., s = 2.6 in.
Use the given degree of confidence and sample data to find(a) The margin of error(b) The confidence interval for the population mean µ.Grade-point averages: 99% confidence; n = 75, = 2.76, s = 0.88
Use the given degree of confidence and sample data to find(a) The margin of error(b) The confidence interval for the population mean µ.Test scores: 90% confidence; n = 150, = 77.6, s = 14.2
Use the given degree of confidence and sample data to find(a) The margin of error(b) The confidence interval for the population mean µ.Cost of basic phone service: 92% confidence; n = 64, = $15.30, s = $1.25
A sample of 35 skulls is obtained for Egyptian males who lived around 1850 BCE. The maximum breadth of each skull is measured with the result that x = 134.5 mm and s = 3.48 mm (based on data from Ancient Races of the Thebaid by Thomson and Randall-Maciver). Using these sample results, construct a
Find the critical value tα/2 that corresponds to the given degree of confidence and sample size n. 99 %; n = 10
Be sure to determine correctly whether the confidence intervals are calculated with the normal distribution or the t distribution.Data Set 18 in Appendix B includes 18 body temperatures. Suppose that we have only the first 10 temperatures given below. For these scores, = 36.36 and s = 0.35.
Be sure to determine correctly whether the confidence intervals are calculated with the normal distribution or the t distribution.In a time-use study, 20 randomly selected managers were found to spend a mean of 2.40 h each day on paperwork. The standard deviation of the 20 scores is 1.30 h (based
Be sure to determine correctly whether the confidence intervals are calculated with the normal distribution or the t distribution.In a study relating the amounts of time required for room-service delivery at a newly opened Radisson Hotel, 20 deliveries had a mean time of 24.2 min and a standard
Be sure to determine correctly whether the confidence intervals are calculated with the normal distribution or the t distribution.In a study relating physical attractiveness and mental disorders, 231 subjects were rated for attractiveness. The resulting sample mean and standard deviation for that
Be sure to determine correctly whether the confidence intervals are calculated with the normal distribution or the t distribution.A survey was conducted to estimate the annual income of CEOs of large corporations. Twenty companies were surveyed and the mean income for this group was $220,000 with a
Be sure to determine correctly whether the confidence intervals are calculated with the normal distribution or the t distribution.A manufacturer of AAA batteries wants to estimate the mean life expectancy of the batteries. A sample of 25 such batteries shows that the distribution of life
Be sure to determine correctly whether the confidence intervals are calculated with the normal distribution or the t distribution.Off-season football players often participate in community events and charity fundraisers. Suppose a firm is bidding to provide T-shirts for players who are representing
Be sure to determine correctly whether the confidence intervals are calculated with the normal distribution or the t distribution.In a study of the use of hypnosis to relieve pain, sensory ratings were measured for 16 subjects, with the results given below (based on data from "An Analysis of
Be sure to determine correctly whether the confidence intervals are calculated with the normal distribution or the t distribution.Refer to Data Set 11 in Appendix B and use only the sample of red M&M plain candies to construct a 95% confidence interval for the mean weight of all M&Ms.
Be sure to determine correctly whether the confidence intervals are calculated with the normal distribution or the t distribution.Refer to Data Set 11 in Appendix B and use the entire sample of 100 plain M&M candies to construct a 95% confidence interval for the mean weight of all M&Ms. how
Find the critical value tα/2 that corresponds to the given degree of confidence and sample size n. 95 %; n = 16
Be sure to determine correctly whether the confidence intervals are calculated with the normal distribution or the t distribution. Refer to Data Set 10 in Appendix B. a. Construct a 95% confidence interval for the mean annual return over three years of U.S. equity funds. b. Construct a 95%
Assume that a small (n ≤ 30) sample is randomly selected from a normally distributed population for which σ is unknown. Construction of a confidence interval should use the t distribution, but how are the confidence interval limits affected if the normal distribution is incorrectly used instead?
A confidence interval is constructed for a small sample of temperatures (in degrees Celsius) randomly selected from a normally distributed population for which σ is unknown (such as the data set given in Exercise 10).a. How is the margin of error E affected if each temperature is converted to the
A simple random sample of Boeing 747 aircraft is selected, and the times (in hours) required to test for structural stress fractures are as follows: 8.1, 9.9, 9.5, 6.9, 9.8. Based on these results, a confidence interval is found to be µ = 8.84 ± 1.24. Find the degree of confidence.
Find the critical value tα/2 that corresponds to the given degree of confidence and sample size n. 98 %; n = 21
Find the critical value tα/2 that corresponds to the given degree of confidence and sample size n. 90 %; n = 8
Use the given degree of confidence and sample data to find(a) The margin of error(b) The confidence interval for the population mean µ. In each case, assume that the population has a normal distribution.Heights of female students: 95% confidence; n = 10, = 64.2 in., s = 2.6 in.
Use the given degree of confidence and sample data to find(a) The margin of error(b) The confidence interval for the population mean µ. In each case, assume that the population has a normal distribution.Grade-point averages: 99% confidence; n = 15, = 2.76, s = 0.88
Use the given degree of confidence and sample data to find(a) The margin of error(b) The confidence interval for the population mean µ. In each case, assume that the population has a normal distribution.Test scores: 90% confidence; n = 16, = 77.6, s = 14.2
Use the given degree of confidence and sample data to find(a) The margin of error(b) The confidence interval for the population mean µ. In each case, assume that the population has a normal distribution.Cost of basic phone service: 98% confidence; n = 19, = $15.30, s = $1.25
Be sure to determine correctly whether the confidence intervals are calculated with the normal distribution or the t distribution.In crash tests of 15 Honda Odyssey minivans, collision repair costs are found to have a distribution that is roughly bell-shaped, with a mean of $1786 and a standard
Assume that a sample is used to estimate a population proportion p. Find the margin of error that corresponds to the given values of n and x and the degree of confidence.n = 800, x = 200, 95%
Use the given data to find the minimum sample size required to estimate a population proportion or percentage.Margin of error: 0.01; confidence level: 90%; and unknown
Use the given data to find the minimum sample size required to estimate a population proportion or percentage.Margin of error: four percentage points; confidence level: 99%; is estimated to be 0.20 from a prior study
Use the given data to find the minimum sample size required to estimate a population proportion or percentage.Margin of error: two percentage points; confidence level: 97%; is estimated to be 0.85 from a prior study
Wawanesa Mutual Insurance Company wanted to estimate the percentage of drivers who changed tapes or CDs while driving. A random sample of 850 drivers resulted in 544 who changed tapes or CDs while driving (based on data from Prevention magazine).a. Find the point estimate of the percentage of all
When 160 CEOs in British Columbia are randomly selected and surveyed, it is found that 41 of them possess an MBA.a. Find the point estimate of the true proportion of all CEOs in British Columbia who possess an MBA.b. Find a 95% confidence interval for the true proportion of all CEOs in British
The drug Ziac is used to treat hypertension. In a clinical test, 3.2% of 221 Ziac users experienced dizziness (based on data from Lederle Laboratories).a. Construct a 99% confidence interval estimate of the percentage of all Ziac users who experience dizziness.b. In the same clinical test, people
In a follow-up article on Y2K problems, a reporter wants to conduct a survey of small businesses, in order to estimate the true proportion of small businesses that took some action regarding the Y2K problem-that is, the then-widespread concern that when the date 2000 arrived, it would confuse
A random survey of 85 CEOs in British Columbia showed 70 respondents have a computer on their desk. Based on those results, construct a 98% confidence interval for the percentage of all CEOs in British Columbia who have a computer on their desk.
Internationally, 53.3% of the candidates who wrote the Certified General Accounting (CGA) exams in December 1995 passed. In Manitoba, out of 781 candidates who wrote those exams, 439 passed (based on data from the Certified General Accountants Association of Manitoba). Assuming that these 1995
The Greybar Tax Company believes that its clients are selected for audits at a rate substantially higher than the rate for the general population. Suppose that the Canada Revenue Agency audits 4.3% of those who earn more than $100,000, but a check of 400 randomly selected Greybar returns with
Assume that a sample is used to estimate a population proportion p. Find the margin of error that corresponds to the given values of n and x and the degree of confidence.n = 1400, x = 420, 99%
The Locust Tree Restaurant keeps records of reservations and no-shows. When 150 Saturday reservations are randomly selected, it is found that 70 of them were no-shows (based on data from American Express). Using a 90% degree of confidence, find a confidence interval for the proportion of Saturday
How many TV households must Nielsen survey to estimate the percentage that are tuned to The Late Show with David Letterman? Assume that you want 97% confidence that your sample percentage has a margin of error of two percentage points. Also assume that nothing is known about the percentage of
The Western Canada Communications Company is considering a bid to provide long-distance phone service. You are asked to conduct a poll to estimate the percentage of consumers who are satisfied with their current long-distance phone service. You want to be 90% confident that your sample percentage
A hotel chain gives an aptitude test to job applicants and considers a multiple-choice test question to be easy if at least 80% of the responses are correct. A random sample of 6503 responses to one particular question includes 84% correct responses. Construct the 99% confidence interval for the
A random sample of 400 people is taken from a large city in Atlantic Canada. They are asked about their views on the amalgamation of the four provinces in Atlantic Canada. Of the respondents, 190 are in favour of this amalgamation. Construct the 98% confidence interval for the true percentage of
In a study of store checkout scanners, 1234 items were checked and 20 of them were found to be overcharges (based on data from "UPC Scanner Pricing Systems: Are They Accurate?" by Goodstein, Journal of Marketing, Vol. 58).a. Using the sample data, construct a 95% confidence interval for the
A health study involves 1000 randomly selected deaths, with 273 of them caused by heart disease (based on data from Statistics Canada).a. Using the sample data, construct a 99% confidence interval for the proportion of all deaths caused by heart disease.b. Use the sample data as a pilot study and
A climatologist claims that half of Canada's largest towns and cities receive more than 200 cm of snowfall each year. Refer to Data Set 4 in Appendix B and construct the 95% confidence interval for the percentage of cities with snowfall over 200 cm. Is the resulting confidence interval consistent
Refer to Data Set 11 in Appendix B and find the sample proportion of M&Ms that are red. Use that result to construct a 95% confidence interval estimate of the population percentage of M&Ms that are red. Is the result consistent with the 20% rate that is reported by the candy maker Mars?

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