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mathematics
statistics

Questions and Answers of Statistics

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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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,
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
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
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
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
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
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).
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
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
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
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.
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
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
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%
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
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
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
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
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
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
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
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
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
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,
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
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
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
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
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, =
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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%
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
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
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
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
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 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
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
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
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

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