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mathematics
statistics

Questions and Answers of Statistics

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
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'
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'
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'
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'
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
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
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
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
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
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
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
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
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
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
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
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 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
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
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
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
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
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
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
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
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,
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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.
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
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
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
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
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
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 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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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 >
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
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 (-
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
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
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
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
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
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
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
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
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

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