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Elementary Statistics 3rd Canadian Edition Mario F. Triola - Solutions
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.Assume that z scores are
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. For a standard normal
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. In a manufacturing
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. In a certain region,
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 and 3.007
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 and - 2.331
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 and - 1.28
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 2.58
Assume that the heights of female students are normally distributed with a mean given by µ = 64.2 in. and a standard deviation given by σ = 2.6 in. (based on data from a survey of college students). Also assume that a female student is randomly selected. Draw a graph, and find the indicated
Based on the sample results in Data Set 18 of Appendix B, assume that human body temperatures are normally distributed with a mean of 36.4°C and a standard deviation of 0.62°C. If we define a fever to be a body temperature above 37.8°C, what percentage of normal and healthy persons would be
One classic use of the normal distribution is inspired by a letter to Dear Abby in which a wife claimed to have given birth 308 days after a brief visit from her husband, who was serving in the Navy. The lengths of pregnancies are normally distributed with a mean of 268 days and a standard
Lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. If we stipulate that a baby is premature if born at least three weeks early, what percentages of babies are born prematurely? Why would this information be useful to hospital administrators?
Based on daily summaries from a Calgary observatory (for January to November 2000), the mean daily counting rates for cosmic rays are approximately normally distributed, with a mean equal to 3465.5 and a standard deviation of 127.7. If one day is randomly selected, what is the probability that the
According to the International Mass Retail Association, girls aged 13 to 17 spend an average of $31.20 on shopping trips in a month. Assume that the amounts are normally distributed with a standard deviation of $8.27. If a girl in that age category is randomly selected, what is the probability that
IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. Mensa is an organization for people with high IQs, and eligibility requires an IQ above 131.5. a. If someone is randomly selected, find the probability that he or she meets the Mensa requirement. b. In a typical
An IBM subcontractor was hired to make ceramic substrates that are used to distribute power and signals to and from computer silicon chips. Specifications require resistance between 1.500 ohms and 2.500 ohms, but the population has normally distributed resistances with a mean of 1.978 ohms and a
The average household expenditure in Canada on postsecondary books is $53.00, with a standard deviation of $18.61 (based on a study by Statistics Canada on family expenditures). If a household is selected at random, find the probability that its expenditure on postsecondary books is between $60.00
Measurements of human skulls from different epochs are analyzed to determine whether they change over time. The maximum breadth is measured for skulls from Egyptian males who lived around 3300 BCE. Results show that those breadths are normally distributed with a mean of 132.6 mm and a standard
According to a national health survey, the serum cholesterol levels of men aged 18 to 24 are normally distributed with a mean and standard deviation (in mg/100mL) of 178.1 and 40.7, respectively. One criterion for identifying risk of coronary disease is a cholesterol level above 300. If a man aged
Assume that the heights of female students are normally distributed with a mean given by µ = 64.2 in. and a standard deviation given by σ = 2.6 in. (based on data from a survey of college students). Also assume that a female student is randomly selected. Draw a graph, and find the indicated
Some vending machines are designed so that their owners can adjust the weights of the quarters that are accepted. If many counterfeit coins are found, adjustments are made to reject more coins, with the effect that most of the counterfeit coins are rejected along with many legal coins. Assume that
Refer to the indicated data set in Appendix B.a. Construct a histogram to determine whether the data set has a normal distribution.b. Find the sample mean and sample standard deviation s.c. Use the sample mean as an estimate of the population mean µ, use the sample standard deviation as an
Refer to the indicated data set in Appendix B.a. Construct a histogram to determine whether the data set has a normal distribution.b. Find the sample mean and sample standard deviation s.c. Use the sample mean as an estimate of the population mean µ, use the sample standard deviation as an
Refer to the indicated data set in Appendix B.a. Construct a histogram to determine whether the data set has a normal distribution.b. Find the sample mean and sample standard deviation s.c. Use the sample mean as an estimate of the population mean µ, use the sample standard deviation as an
When you constructed a histogram for total weights of discarded garbage, for Question 22, was the distribution exactly normal? If not, do you believe your probability estimate in Question 22 was likely too low or too high? Explain.
Assume that the heights of female students are normally distributed with a mean given by µ = 64.2 in. and a standard deviation given by σ = 2.6 in. (based on data from a survey of college students). Also assume that a female student is randomly selected. Draw a graph, and find the indicated
Assume that the heights of female students are normally distributed with a mean given by µ = 64.2 in. and a standard deviation given by σ = 2.6 in. (based on data from a survey of college students). Also assume that a female student is randomly selected. Draw a graph, and find the indicated
Assume that the heights of female students are normally distributed with a mean given by µ = 64.2 in. and a standard deviation given by σ = 2.6 in. (based on data from a survey of college students). Also assume that a female student is randomly selected. Draw a graph, and find the indicated
Assume that the heights of female students are normally distributed with a mean given by µ = 64.2 in. and a standard deviation given by σ = 2.6 in. (based on data from a survey of college students). Also assume that a female student is randomly selected. Draw a graph, and find the indicated
Replacement times for TV sets are normally distributed with a mean of 8.2 years and a standard deviation of 1.1 years (based on data from "Getting Things Fixed," Consumer Reports). Find the probability that a randomly selected TV set will have a replacement time of less than 7.0 years.
Replacement times for CD players are normally distributed with a mean of 7.1 years and a standard deviation of 1.4 years (based on data from "Getting Things Fixed," Consumer Reports). Find the probability that a randomly selected CD player will have a replacement time of less than 8.0 years.
Assume that the heights of soldiers in the Canadian Armed Forces are normally distributed with a mean height of 70.3 in. and a standard deviation of 3.4 in. Find the probability of one soldier who is selected at random having a height of 77.0 in. or greater.
Assume that female college students have heights that are normally distributed with a mean of 64.2 in. and a standard deviation of 2.6 in. Find the height for the given percentile. P85
According to the Opinion Research Corporation, men spend an average of 11.4 min in the shower. Assume that the times are normally distributed with a standard deviation of 1.8 min. Find the values of the quartiles Q1 and Q3.
IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. If we define a genius to be someone in the top 1% of IQ scores, find the score separating geniuses from the rest of us. Are there any jobs where this score could reasonably be used as one criterion for employment?
A subcontractor manufactures ceramic substrates for IBM. These devices have resistances that are normally distributed with a mean of 1.978 ohms and a standard deviation of 0.172 ohms. If the required specifications are to be modified so that 3% of the devices are rejected because their resistances
Scores obtained from the Law School Admission Test (LSAT) are normally distributed with a mean score of 550 and a standard deviation of 110. a. If a test score is selected at random, find the probability that it is less than 750. b. If the top 16% of the test scores are usually good enough for
Measurements of human skulls from different epochs are analyzed to determine whether they change over time. The maximum breadth is measured for skulls from Egyptian males who lived around 3300 BCE. Results show that those breadths are normally distributed with a mean of 132.6 mm and a standard
Based on daily summaries from a Calgary observatory over a period of ten months, the mean daily counting rates for cosmic rays are approximately normally distributed, with a mean equal to 3465.5 and a standard deviation of 127.7. Find the sixth decile D6. What is the mean daily counting rate that
Quarters have weights that are normally distributed with a mean of 5.67 g and a standard deviation of 0.070 g. a. If a vending machine is adjusted to reject quarters weighing less than 5.53 g or more than 5.81 g, what is the percentage of legal quarters that are rejected? b. Find the weights of
The construction of a histogram for a data set reveals that the distribution is approximately normal and the box plot is constructed with these quartiles: Q1 = 62, Q2 = 70, Q3 = 78. Estimate the standard deviation.
An instructor informs her physics class that a test is very difficult, but the grades will be curved. Scores for the test are normally distributed with a mean of 25 and a standard deviation of 5. a. If she curves by adding 50 to each grade, what is the new mean? What is the new standard
According to data from the College Entrance Examination Board, the mean math SAT score is 475 and 17.0% of the scores are above 600. Find the standard deviation, and then use that result to find the 99th percentile. (Assume that the scores are normally distributed.)
Assume that female college students have heights that are normally distributed with a mean of 64.2 in. and a standard deviation of 2.6 in. Find the height for the given percentile. P66
The College Entrance Examination Board writes that "for the SAT Achievement Tests, your score would fall in a range [between] about 30 points above [and| below your actual ability about two-thirds of the time. This range is called the standard error of measurement (SEM)." Use that statement to
Assume that female college students have heights that are normally distributed with a mean of 64.2 in. and a standard deviation of 2.6 in. Find the height for the given percentile. P15
Assume that female college students have heights that are normally distributed with a mean of 64.2 in. and a standard deviation of 2.6 in. Find the height for the given percentile. P35
Replacement times for TV sets are normally distributed with a mean of 8.2 years and a standard deviation of 1.1 years (based on data from "Getting Things Fixed," Consumer Reports). a. Find the replacement time that separates the top 20% from the bottom 80%. b. Find the probability that a randomly
Replacement times for CD players are normally distributed with a mean of 7.1 years and a standard deviation of 1.4 years (based on data from "Getting Things Fixed," Consumer Reports). Find P55, which is the replacement time separating the top 45% from the bottom 55%.
Weights of paper discarded by households each week are normally distributed with a mean of 4.3 kg and a standard deviation of 1.9 kg. Find P33, which is the weight that separates the bottom 33% from the top 67%.
Based on the sample results in Data Set 18 of Appendix B, assume that human body temperatures are normally distributed with a mean of 36.4°C and a standard deviation of 0.62°C. What two temperature levels separate the bottom 2% and the top 2%? Could these values serve as reasonable limits that
The durations of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. If we stipulate that a baby is premature if the length of pregnancy is in the lowest 4%, find the duration that separates premature babies from those who are not premature.
Assume that female students' heights are normally distributed with a mean given by µ = 64.2 in and a standard deviation given by σ = 2.6 in. a. If one female student is randomly selected, find the probability that her height is between 64.2 in and 65.2 in. b. If 36 female students are randomly
The depth of a diamond signifies 100 times the ratio of its height to its diameter. For many high-priced diamonds, depth appears to be normally distributed, with a mean of 60.83 and a standard deviation of 1.97 (based on Data Set 21 in Appendix B). If 40 high-priced diamonds are randomly selected,
The ages of U.S. commercial aircraft have a mean of 13.0 years and a standard deviation of 7.9 years (based on data from Aviation Data Services). If the Federal Aviation Administration randomly selects 35 commercial aircraft for special stress tests, find the probability that the mean age of this
Information provided by Bell Canada in Winnipeg showed that the average monthly bill for basic service was normally distributed with a mean of $15.30 and a standard deviation of $1.25. If 55 phone bills are randomly selected, find the probability that their mean exceeds $15.
The typical computer random-number generator yields numbers in a uniform distribution between 0 and 1 with a mean of 0.500 and a standard deviation of 0.289. If 45 random numbers are generated, find the probability that their mean is below 0.565.
A study was made of seat-belt use among children who were involved in car crashes that caused them to be hospitalized. It was found that children not wearing any restraints had hospital stays with a mean of 7.37 days and a standard deviation of 0.79 day. If 40 such children are randomly selected,
As part of his review for a chemistry test, a student randomly selects (without replacement) 40 out of the 102 elements listed on the standard tables, and tries to guess their atomic numbers. Given that the mean of all 102 atomic numbers is 51.794, and the population standard deviation is 29.804,
SAT verbal scores are normally distributed with a mean of 430 and a standard deviation of 120 (based on data from the College Board ATP). Randomly selected SAT verbal scores are obtained from the population of students who took a test preparatory course from a training school. Assume that this
The lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. a. If one pregnant female is randomly selected, find the probability that her length of pregnancy is less than 260 days. b. If 25 randomly selected females are put on a special diet just
A survey by Statistics Canada shows the average household expenditure on post-secondary textbooks is $53.00, with a standard deviation of $18.61. A similar poll randomly selects 150 households to find average expenditure on post-secondary textbooks. a. Find the probability that the mean is greater
M&M plain candies have a mean weight of 0.9147 g and a standard deviation of 0.0369 g (based on Data Set 11 in Appendix B). The M&M candies used in Data Set 11 came from a package containing 1498 candies, and the package label stated that the net weight is 48.0 oz, or 1361 g. (If every package has
Assume that female students' heights are normally distributed with a mean given by µ = 64.2 in and a standard deviation given by σ = 2.6 in. a. If one female student is randomly selected, find the probability that her height is above 63.0 in. b. If 100 female students are randomly selected, find
Weights of players in offensive back positions (including quarterback) in the Canadian Football League are approximately normally distributed, with a mean of 197.5 lb and a standard deviation of 14.2 lb (based on data from the CFL website). An elevator at the hotel that is hosting an awards dinner
A population consists of these scores: 2, 3, 6, 8, 11, 18.a. Find µ and σ.b. List all samples of size n = 2 that are obtained without replacement.c. Find the population of all values of x by finding the mean of each sample from part (b).d. Find the mean µ and standard deviation σ for the
An education researcher develops an index of academic interest and obtains scores for a randomly selected sample of 350 college students. The results are summarized in the accompanying box plot. If 15 of the students are randomly selected, find the probability that their mean score is greater than
The finite population correction factor can be ignored when sampling with replacement or when n ≤ 0.05N. When collecting a sample (without replacement) that is 5% of the population N, what do the values of the finite population correction factor have in common for values of N > 600? (That is, try
Assume that female students' heights are normally distributed with a mean given by µ = 64.2 in and a standard deviation given by σ = 2.6 in. a. If one female student is randomly selected, find the probability that her height is above 65.0 in. b. If 50 female students are randomly selected, find
Assume that female students' heights are normally distributed with a mean given by µ = 64.2 in and a standard deviation given by σ = 2.6 in. a. If 4 female students are randomly selected, find the probability that their mean height is between 63.0 in and 65.0 in. b. Why can the central limit
Replacement times for TV sets are normally distributed with a mean of 8.2 years and a standard deviation of 1.1 years (based on data from "Getting Things Fixed," Consumer Reports). Find the probability that 40 randomly selected TV sets will have a mean replacement time less than 8.0 years.
Replacement times for CD players are normally distributed with a mean of 7.1 years and a standard deviation of 1.4 years (based on data from "Getting Things Fixed," Consumer Reports). Find the probability that 45 randomly selected CD players will have a mean replacement time of 6.8 years or less.
The total weights of garbage that households discard weekly is approximately normally distributed, with a mean of 12.5 kg and a standard deviation of 5.7 kg (based on Data Set 1 in Appendix B).s a. If 120 households are randomly selected, find the probability that the mean weight of their discarded
According to the International Mass Retail Association, girls aged 13 to 17 spend an average of $31.20 on shopping trips in a month. Assume that the amounts have a standard deviation of $8.27. If 85 girls in that age category are randomly selected, what is the probability that their mean monthly
For females aged 18-24, systolic blood pressures (in mm Hg) are normally distributed with a mean of 114.8 and a standard deviation of 13.1. a. If a woman between the ages of 18 and 24 is randomly selected, find the probability that her systolic blood pressure is above 120. b. If 12 women in that
Do the following: a. Find the indicated binomial probability using Table A-l in Appendix A. If np ≥ 5 and nq ≥ 5, also estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution; if np < 5 or nq < 5, then state that the normal
Do the following: a. Find the indicated binomial probability using Table A-l in Appendix A. If np ≥ 5 and nq ≥ 5, also estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution; if np < 5 or nq < 5, then state that the normal
Do the following: a. Find the indicated binomial probability using Table A-l in Appendix A. If np ≥ 5 and nq ≥ 5, also estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution; if np < 5 or nq < 5, then state that the normal
Estimate the probability of getting at least 55 girls in 100 births.
Estimate the probability of getting exactly 32 boys in 64 births.
Estimate the probability of passing a true/false test of 50 questions if 60% (or 30 correct responses) represents a passing grade and all responses are random guesses.
A multiple-choice test consists of 50 questions with possible answers of a, b, c, d, and e. Estimate the probability of getting at most 30% correct if all answers are random guesses.
Based on past records, there is a 3.62% chance that any particular CFL player is a punter or kicker. For 140 randomly selected players, estimate the probability that exactly 3 are punters or kickers.
The Angus Reid Group surveyed Ontario residents on what they think will be the most valuable type of education to have in the work force ten years from now. Thirty-five percent of the respondents chose a college diploma in technical occupations. Estimate the probability that if 1000 Ontario
According to a consumer affairs representative from Mars (the candy company, not the planet), 10% of all M&M plain candies are blue. Data Set 11 in Appendix B shows that among 100 M&Ms chosen, 5 are blue. Estimate the probability of randomly selecting 100 M&Ms and getting 5 or fewer that are blue.
John Dukhia plans to place 200 bets of $1 each on the number 7 at roulette. On any one spin there is a probability of 1/38 that 7 will be the winning number. For John to end up with a profit, the number 7 must occur at least 6 times among the 200 trials. Estimate the probability that John finishes
The Angus Reid Group surveyed Ontario residents on what they think will be the most valuable type of education to have in the work force ten years from now. Eighteen percent of the respondents chose a university degree in science. Estimate the probability that if 400 Ontario residents are selected
Air Borealis has been experiencing a 7% rate of no-shows on advance reservations. In a test project that requires passengers to confirm reservations, it is found that among 250 randomly selected advance reservations, there are 4 no-shows. Assuming that the confirmation requirement has no effect so
In a survey, the Canadian Automobile Association (CAA) found that 38% of respondents had bought used vehicles. A car dealership surveys 150 people at random and finds that 45 of them have bought used vehicles. Estimate the probability of 45 or more respondents being used-vehicle purchasers. Based
A successful venture capital firm reports that it finances only 10% of the proposals that it receives. A check of 100 randomly selected proposals shows that 8 of them were financed by the firm. Estimate the probability that among 100 proposals, 8 or fewer were financed by the firm. Based on the
A manufacturer of automobile headlights claims that 10% of a batch of these headlights are defective. A quality control inspector tests a random selection of 300 headlights in the batch. The number of defective headlights in this random sample is 35, which is more than expected. Estimate the
Some couples have genetic characteristics configured so that one-quarter of all offspring have blue eyes. A study is conducted of 40 couples believed to have those characteristics, with the result that 8 of their 40 offspring have blue eyes. Estimate the probability that among 40 offspring, 8 or
Sunnybrook Hospital is conducting a blood drive because its supply of group O blood is low, and it needs 177 donors of group O blood. If 400 volunteers donate blood, estimate the probability that the number with group O blood is at least 177. Forty-six percent of us have group O blood, according to
Some companies monitor quality by using a method of acceptance sampling whereby an entire batch of items is rejected if, in a random sample, the number of defects is at least some predetermined number. The Macker Machine Company buys machine bolts in batches of 5000 and rejects a batch if, when 50
Replacement times for TV sets are normally distributed with a mean of 8.2 years and a standard deviation of 1.1 years (based on data from "Getting Things Fixed," Consumer Reports). Estimate the probability that for 250 randomly selected TV sets, at least 15 of them have replacement times greater
Assume that a baseball player hits .350, so his probability of a hit is 0.350. (Ignore the complications caused by walks.) Also assume that his hitting attempts are independent of each other. a. Find the probability of at least 1 hit in 4 tries in 1 game. b. Assuming that this batter gets up to bat
Find the difference between the answers obtained with and without use of the continuity correction in each of the following. What do you conclude from the results?a. Estimate the probability of getting at least 11 girls in 20 births.b. Estimate the probability of getting at least 22 girls in 40
Air Borealis works only with advance reservations and experiences a 7% rate of no-shows. How many reservations could be accepted for an airliner with a capacity of 250 if there is at least a 0.95 probability that all reservation holders who show will be accommodated?
Do the following: a. Find the indicated binomial probability using Table A-l in Appendix A. If np ≥ 5 and nq ≥ 5, also estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution; if np < 5 or nq < 5, then state that the normal
Suppose that a gas pipeline averages 1 blemish per 40 km. Find the following probabilities for a section of the pipeline. More than 60 km between successive blemishes if there is at least 40 km between successive blemishes
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