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statistics

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

Assume that in a procedure that yields a binomial distribution, a trial is repeated n times. Find the probability of x successes given the probability p of success on a single trial. Use the given values of n, x, and p and the binomial probability formula or statistical software. n = 8, x = 6, p =
Refer to the table in the margin for n = 8 and p = 0.381. When a car buyer is selected at random, there is a 0.381 probability that he or she bought a used car (based on data from a CAA members' survey). In each case, assume that 8 buyers are randomly selected and find the indicated
Refer to the table in the margin for n = 8 and p = 0.381. When a car buyer is selected at random, there is a 0.381 probability that he or she bought a used car (based on data from a CAA members' survey). In each case, assume that 8 buyers are randomly selected and find the indicated
Refer to the table in the margin for n = 8 and p = 0.381. When a car buyer is selected at random, there is a 0.381 probability that he or she bought a used car (based on data from a CAA members' survey). In each case, assume that 8 buyers are randomly selected and find the indicated
Refer to the table in the margin for n = 8 and p = 0.381. When a car buyer is selected at random, there is a 0.381 probability that he or she bought a used car (based on data from a CAA members' survey). In each case, assume that 8 buyers are randomly selected and find the indicated
Assume that male and female births are equally likely and that the birth of any child does not affect the probability of the gender of any other children. Find the probability of a. Exactly 4 girls in 10 births. b. At least 4 girls in 10 births. c. Exactly 8 girls in 20 births.
According to a market-share study, 13% of televisions in use are tuned to Hockey Night in Canada on Saturday night. Assume that an advertiser wants to verify that 13% market share value by conducting its own survey, and a pilot survey begins with 20 households having TV sets in use at the time of a
Mars, Inc. claims that 20% of its plain M&M candies are red. Find the probability that when 15 plain M&M candies are randomly selected, exactly 20% (or 3 candies) are red.
In a market study for Zellers, a researcher found that 76% of customers are repeat customers. If 12 customers are selected at random, find the probability that at least 11 of them are repeat customers. Suppose at least 11 of the 12 are repeat customers; does it appear that the 76% value found in
A statistics quiz consists of 10 multiple-choice questions, each with 5 possible answers. For someone who makes random guesses for all of the answers, find the probability of passing if the minimum passing grade is 60%. Is the probability high enough to make it worth the risk of passing by random
A regional airline has a policy of booking as many as 15 persons on an airplane that can seat only 14. (Past studies have revealed that only 85% of the booked passengers actually arrive for the flight.) Find the probability that if the airline books 15 persons, not enough seats will be available.
In a survey, the Canadian Automobile Association (CAA) found that 6.1% of its members bought their cars at a used-car lot. If 15 CAA members are selected at random, what is the probability that 4 of them bought their cars at a used-car lot?
Deloitte Touche Tohamatsu surveyed British Columbia's top CEOs. According to the survey, 82% of the respondents like to have a computer on their desk. Suppose that a conference is being arranged in Montreal for 9 of these CEOs. Unfortunately there are only 7 computers available for their
A quality control manager at the Don Mills Electronics Company knows that his company has been making surge protectors with a 10% rate of defective units. He has instituted several measures designed to lower that defect rate. In a test of 20 randomly selected surge protectors, only one is found to
The Telektronic Company purchases large shipments of fluorescent bulbs and uses this acceptance sampling plan: Randomly select and test 24 bulbs, then accept the whole batch if there is only 1 or none that doesn't work. If a particular shipment of thousands of bulbs actually has a 4% rate of
A survey of college statistics students shows that 30% of the students who show up for their 8:00 a.m. classes are late. One statistics professor reports that among 15 of her students selected at random, only 3 were late for her 8:00 a.m. class. Find the probability that this number will be that
Nine percent of men and 0.25% of women cannot distinguish between the colours red and green. This is the type of colour blindness that causes problems with traffic signals. If 6 men are randomly selected for a study of traffic signal perceptions, find the probability that exactly 2 of them cannot
A student experiences difficulties with malfunctioning alarm clocks. Instead of using one alarm clock, he decides to use three. What is the probability that at least one alarm clock works correctly if each individual alarm clock has a 98% chance of working correctly?
If a procedure meets all the conditions of a binomial distribution except that the number of trials is not fixed, then the geometric distribution can be used. The probability of getting the first success on the xth trial is given by P(x) = p(l - p)x-1 where p is the probability of success on any
The binomial distribution applies only to cases involving two types of outcomes, whereas the multinomial distribution involves more than two categories. It is helpful to develop the technical skill to calculate means and standard deviations, but it is especially important to develop an ability to
Sampling (without replacement) a randomly selected group of 12 different tires from a population of 30 tires that includes 5 that are defective
Find the mean µ, variance σ2, and standard deviation σ for the given values of n and p. Assume the binomial conditions are satisfied in each case. n = 64, p = 0.5
A report to Health Canada indicated that the rate of lung cancer development among males is 9.1%. In one region, an intensive education program is used in an attempt to lower that rate. After running the program, a long-term follow-up study of 200 males is conducted. Consider as unusual any result
Maclean's conducted a marketing solutions poll of mutual funds and fund owners. One question asked fund owners what action they took after the October 1997 market drop. Seventeen percent of respondents said they bought more funds. Consider as unusual any result that differs from the mean by more
According to the same Maclean's poll as in Exercise 11, fund owners were asked what they believe will happen to the stock market over the next year. In answer to the question, 46% stated that they believe the market will rise. Assume that this poll was conducted among 900 fund owners. Consider as
According to the CBC, 2.539 million Canadians watched the 1997 Grey Cup game. This figure represents a market share of 29%: that is, 29% of televisions were tuned to the game. Assume that this game is being broadcast and 4000 televisions are randomly selected. Consider as unusual any result that
A Calgary observatory records daily the mean counting rates for cosmic rays for that day. If a daily mean rate below 3200 is considered low, then "low" values occur about 3.6% of the time (in no particular sequence). Suppose a sample of 90 mean daily counting rates is randomly selected. Consider as
Statistics Canada reports that 27.3% of all deaths are attributable to heart disease. Consider as unusual any result that differs from the mean by more than two standard deviations. That is, unusual values are either less than σ - 2σ or greater than µ + 2σ. a. Find the mean and standard
One test of extrasensory perception involves the determination of a shape. Fifty blindfolded subjects are asked to identify the one shape selected from the possibilities of a square, circle, triangle, star, heart, and profile of former Prime Minister Paul Martin. Consider as unusual any result that
The Port Arthur Computer Supply Company knows that 16% of its computers will require warranty repairs within one month of shipment. In a typical month, 279 computers are shipped. a. If x is the random variable representing the number of computers requiring warranty repairs among the 279 sold in one
a. If a company makes a product with an 80% yield (meaning that 80% are good), what is the minimum number of items that must be produced to be at least 99% sure that the company produces at least 5 good items? b. If the company produces batches of items, each with the minimum number determined in
Find the mean µ, variance σ2, and standard deviation σ for the given values of n and p. Assume the binomial conditions are satisfied in each case. n = 150, p = 0.4
Find the mean µ, variance σ2, and standard deviation σ for the given values of n and p. Assume the binomial conditions are satisfied in each case. n = 1068, p = 1/4
Find the mean µ, variance σ2, and standard deviation σ for the given values of n and p. Assume the binomial conditions are satisfied in each case. n = 2001, p = 0.221
Several students are unprepared for a true/false test with 25 questions, and all of their answers are guesses. Find the mean, variance, and standard deviation for the number of correct answers that would be expected for such students. Would it be unusual for one of these students to get a good mark
On a multiple-choice test with 50 questions, each question has possible answers of a, b, c, and d, one of which is correct. For students who guess at all answers, find the mean, variance, and standard deviation for the number of correct answers that would be expected. Would it be unusual for one of
The probability of a 7 in roulette is 1/38. In an experiment, the wheel is spun 500 times. If this experiment is repeated many times, find the mean and standard deviation for the number of 7s. Would it be unusual not to win once in 500 trials? Why or why not? Find the indicated values.
The probability of winning Lotto 6/49 is 1/13,983,816. If someone plays 5200 times over 50 years, find the mean and standard deviation for the number of wins. (Express your answer with three significant digits.) Find the indicated values.
When surveyed for brand recognition, 95% of consumers recognize Coke (based on data from Total Research Corporation). A new survey of 1200 randomly selected consumers is to be conducted. For such a group of 1200, consider as unusual any result that differs from the mean by more than two standard
Assume that the Poisson distribution has the indicated mean and use Formula 4-10 to find the probability of the value given for the random variable x. µ = 2, x = 3
For a recent year, there were 46 aircraft hijackings worldwide (based on data from the FAA). Using one day as the specified interval required for a Poisson distribution, we find the mean number of hijackings per day to be estimated as p = 46/365 = 0.126. If the United Nations is organizing a single
A classic example of the Poisson distribution involves the number of deaths caused by horse kicks of men in the Prussian Army between 1875 and 1894. Data for 14 corps were combined for the 20-year period, and the 280 corps-years included a total of 196 deaths. After finding the mean number of
In 1996, there were 572 homicide deaths in Canada (based on data from Statistics Canada). For a randomly selected day, find the probability that the number of homicide deaths is Use the Poisson distribution to find the indicated probabilities. a. 0 b. 1 c. 2 d. 3 e. 4
Assume that a binomial experiment has 15 trials, each with a 0.01 probability of success. Find the probability of getting exactly one success among the 15 trials by using (a) Table A-l and (b) The Poisson distribution as an approximation to the binomial distribution. Note that the rule of thumb
The following is a binomial experiment, but the large number of trials involved creates major problems with many calculators. Overcome that obstacle by approximating the binomial distribution by the Poisson distribution. If you bet on the number 7 for one spin of a roulette wheel, there is a 1/38
Assume that the Poisson distribution has the indicated mean and use Formula 4-10 to find the probability of the value given for the random variable x. µ = 4, x = 1
Assume that the Poisson distribution has the indicated mean and use Formula 4-10 to find the probability of the value given for the random variable x. µ = 0.845, x = 2
Assume that the Poisson distribution has the indicated mean and use Formula 4-10 to find the probability of the value given for the random variable x. µ = 0.250, x = 2
A new tornado-resistant communications tower is being planned for the area around Regina. The area averages 3.25 tornadoes per year. Find the probability that in a one-year period, the number of tornadoes is Use the Poisson distribution to find the indicated probabilities. a. 0 b. 1 c. 4
According to data from a Calgary observatory, the mean daily counting rate for cosmic rays falls below 3000 about one day per month. Find the probability that in a randomly selected month, the number of days with a mean counting rate below 3000 is Use the Poisson distribution to find the indicated
The Townsend Manufacturing Company experiences a weekly average of 0.2 accidents requiring medical attention. Find the probability that in a randomly selected week, the number of accidents requiring medical attention is Use the Poisson distribution to find the indicated probabilities. a. 0 b. 1 c. 2
A statistics professor finds that when she schedules an office hour for student help, an average of 2 students arrive. Find the probability that in a randomly selected office hour, the number of student arrivals is Use the Poisson distribution to find the indicated probabilities. a. 0 b. 2 c. 5
Careful analysis of magnetic computer data tape shows that for each 150 m of tape, the average number of defects is 2.0. Find the probability of more than one defect in a randomly selected length of 150 m of tape. Use the Poisson distribution to find the indicated probabilities.
In Lotto 6/49, a bettor selects 6 numbers from 1 to 49 (without repetition), and a winning 6-number combination is later randomly selected. Find the probability of getting a. All 6 winning numbers b. Exactly 5 of the winning numbers c. Exactly 3 of the winning numbers d. No winning numbers
A quality control manager uses test equipment to detect defective computer modems. A sample of 3 different modems is to be randomly selected from a group consisting of 12 that are defective and 18 that have no defects. What is the probability that (a) all 3 selected modems are defective, and (b) at
A manager can identify employee theft by checking samples of employee shipments. Among 36 employees, 2 are stealing. If the manager checks on 4 different randomly selected employees, find the probability that neither of the thieves will be identified.
An approved jury list contains 20 women and 20 men. Find the probability of randomly selecting 12 of these people and getting an all-male jury. Under these circumstances, if the defendant is convicted by an all-male jury, is there strong evidence to suggest that the jury was not randomly selected?
With one method of acceptance sampling, a sample of items is randomly selected without replacement and the entire batch is rejected if there is at least one defect. The Niko Electronics Company has just manufactured 5000 CDs, and 3% are defective. If 10 of the CDs are selected and tested, find the
a. What is a random variable?b. What is a probability distribution?c. An insurance association's study of home smoke detector use involves homes randomly selected in groups of 4. The accompanying table lists values and probabilities for x, the number of homes (in groups of 4) that have smoke
Fifteen percent of sport/compact cars are dark green (based on data from DuPont Automotive). Assume that 50 sport/compact cars are randomly selected. a. What is the expected number of dark green cars in such a group of 50? b. In such groups of 50, what is the mean number of dark, green cars? c. In
In a survey, the Canadian Automobile Association (CAA) found that 58% of its members paid cash for their vehicles. Ten CAA members are selected at random. a. Find the probability that exactly half of the 10 members paid cash for their vehicles. b. Find the probability that at least half of the 10
Inability to get along with others is the reason cited in 17% of worker firings (based on data from Robert Half International, Inc.). Concerned about her company's working conditions, the personnel manager at the Drummondville Fabric Company plans to investigate the 5 employee firings that occurred
Refer to the data given in Exercise 4. Let the random variable x represent the number of fired employees (among 5) who were let go because of an inability to get along with others. a. Find the mean value of x. b. Find the standard deviation of the random variable x. c. Is it unusual to have 4
The Western Canada Trucking Company operates a large fleet of trucks. Last year, there were 84 breakdowns. a. Find the mean number of breakdowns per day. b. Find the probability that for a randomly selected day, 2 trucks break down.
In setting up a manufacturing process for a new computer memory storage device, the initial configuration has a 16% yield: 16% of the devices are acceptable and 84% are defective. If 12 of the devices are made, what is the probability of getting at least 1 that is good? If it is very important to
The Sports Associates Vending Company supplies refreshments at a baseball stadium and must plan for the possibility of a World Series contest. In the accompanying frequency table (based on past results), x represents the number of baseball games required to complete a World Series contest.a.
A casino cheat is caught trying to use a pair of loaded dice. At his court trial, physical evidence reveals that some of the black dots were drilled, filled with lead, then repainted to appear normal. In addition to the physical evidence, the dice are rolled in court with these results:A
Suppose that the temperature readings for a certain gauge are uniformly distributed between 0°C and 5°C. Find the probability of a randomly selected temperature reading falling in the following range: Between 0.8°C and 4.7°C
Suppose that the temperature readings for a certain gauge are uniformly distributed between 0°C and 5°C. Find the probability of a randomly selected temperature reading falling in the following range: Find the mean and standard deviation for the gauge readings.
Suppose that the amount of paint that goes into a 4-L can is uniformly distributed between 3.85 L and 4.15 L. What is the probability a can has less than 3.9 L?
Suppose that the amount of paint that goes into a 4-L can is uniformly distributed between 3.85 L and 4.15 L. What is the probability a can has more than 4.05 L?
Suppose that the amount of paint that goes into a 4-L can is uniformly distributed between 3.85 L and 4.15 L. Suppose the manufacturer wants the amount of paint in a can to be within 0.5 standard deviations of the mean. Based on the probability of this happening, are these realistic expectations?
For a uniform distribution, show why 100% of the distribution lies within 2 standard deviations of the mean, regardless of the values for a and b with a < b.
Assume that the readings on the thermometers are normally distributed with a mean of 0°C and a standard deviation of l.00°C. A thermometer is randomly selected and tested. In each case, draw a sketch, and find the probability of each reading in degrees. Less than - 1.47
Assume that the readings on the thermometers are normally distributed with a mean of 0°C and a standard deviation of l.00°C. A thermometer is randomly selected and tested. In each case, draw a sketch, and find the probability of each reading in degrees. Less than - 2.09
Assume that the readings on the thermometers are normally distributed with a mean of 0°C and a standard deviation of l.00°C. A thermometer is randomly selected and tested. In each case, draw a sketch, and find the probability of each reading in degrees. Greater than 0.25
Assume that the readings on the thermometers are normally distributed with a mean of 0°C and a standard deviation of l.00°C. A thermometer is randomly selected and tested. In each case, draw a sketch, and find the probability of each reading in degrees. Between 1.34 and 2.67
Assume that the readings on the thermometers are normally distributed with a mean of 0°C and a standard deviation of l.00°C. A thermometer is randomly selected and tested. In each case, draw a sketch, and find the probability of each reading in degrees. Between - 1.72 and - 0.31
Assume that the readings on the thermometers are normally distributed with a mean of 0°C and a standard deviation of l.00°C. A thermometer is randomly selected and tested. In each case, draw a sketch, and find the probability of each reading in degrees. Between - 2.22 and - 1.11
Assume that the readings on the thermometers are normally distributed with a mean of 0°C and a standard deviation of l.00°C. A thermometer is randomly selected and tested. In each case, draw a sketch, and find the probability of each reading in degrees. Between 0.089 and 1.78
Assume that the readings on the thermometers are normally distributed with a mean of 0°C and a standard deviation of l.00°C. A thermometer is randomly selected and tested. In each case, draw a sketch, and find the probability of each reading in degrees. Less than 0.08
Assume that the readings on the thermometers are normally distributed with a mean of 0°C and a standard deviation of l.00°C. A thermometer is randomly selected and tested. In each case, draw a sketch, and find the probability of each reading in degrees. Less than 3.01
Assume that the readings on the thermometers are normally distributed with a mean of 0°C and a standard deviation of l.00°C. A thermometer is randomly selected and tested. In each case, draw a sketch, and find the probability of each reading in degrees. Greater than - 2.29
Assume that the readings on the thermometers are normally distributed with a mean of 0°C and a standard deviation of l.00°C. A thermometer is randomly selected and tested. In each case, draw a sketch, and find the probability of each reading in degrees. Greater than - 1.05
Assume that the readings on the thermometers are normally distributed with a mean of 0°C and a standard deviation of l.00°C. A thermometer is randomly selected and tested. In each case, draw a sketch, and find the probability of each reading in degrees. Between - 1.99 and 2.01
Assume that the readings on the thermometers are normally distributed with a mean of 0°C and a standard deviation of l.00°C. A thermometer is randomly selected and tested. In each case, draw a sketch, and find the probability of each reading in degrees. Between - 0.07 and 2.19
Assume that the readings on the thermometers are normally distributed with a mean of 0°C and a standard deviation of l.00°C. A thermometer is randomly selected and tested. In each case, draw a sketch, and find the probability of each reading in degrees. Between - 1.00 and 4.00
Assume that the readings on the thermometers are normally distributed with a mean of 0°C and a standard deviation of l.00°C. A thermometer is randomly selected and tested. In each case, draw a sketch, and find the probability of each reading in degrees. Between - 5.00 and 2.00
Assume that the readings on the thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. Find the indicated probability, where z is the reading in degrees. P(z > 2.33)
Assume that the readings on the thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. Find the indicated probability, where z is the reading in degrees. P (2.00 < z < 2.50)
Assume that the readings on the thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. Find the indicated probability, where z is the reading in degrees. P (- 3.00 < z < 2.00)
Assume that the readings on the thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. Find the indicated probability, where z is the reading in degrees. P (z < - 1.44)
Assume that the readings on the thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A thermometer is randomly selected and tested. In each case, draw a sketch, and find the temperature reading corresponding to the given information. Find P90, the 90th
Assume that the readings on the thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A thermometer is randomly selected and tested. In each case, draw a sketch, and find the temperature reading corresponding to the given information. Find P30, the 30th
Assume that the readings on the thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A thermometer is randomly selected and tested. In each case, draw a sketch, and find the temperature reading corresponding to the given information. Find Q1 the temperature
Assume that the readings on the thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A thermometer is randomly selected and tested. In each case, draw a sketch, and find the temperature reading corresponding to the given information. Find D1, the
Assume that the readings on the thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A thermometer is randomly selected and tested. In each case, draw a sketch, and find the temperature reading corresponding to the given information. If 4% of the
Assume that the readings on the thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A thermometer is randomly selected and tested. In each case, draw a sketch, and find the temperature reading corresponding to the given information. If 8% of the
Assume that the readings on the thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A thermometer is randomly selected and tested. In each case, draw a sketch, and find the temperature reading corresponding to the given information. A quality control
Assume that the readings on the thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A thermometer is randomly selected and tested. In each case, draw a sketch, and find the temperature reading corresponding to the given information. If 2.5% of the

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