Solved: In Exercise, determine whether the experiment is a

Problem 1CQ Determine whether the random variable x is discrete or continuous. Explain your reasoning. (a) Let x represent the number of lightning strikes that occur in Wyoming during the month of June. (b) Let x represent the amount of fuel (in gallons) used by a jet during takeoff. (c) Let x represent the total number of die rolls required for an individual to roll a five.

Problem 25E During a 12-year period, sharks killed an average of 5 people each year worldwide. Find the probability that the number of people killed by sharks next year is (a) exactly three, (b) more than six, and (c) at most five.

Problem 1E In Exercise, determine whether the random variable x is discrete or continuous. Explain your reasoning. Let x represent the number of pumps in use at a gas station.

Problem 2CQ The table lists the number of computers per household in the United States. Computers 0 1 2 3 4 5 Number of households (in millions) 27 47 24 10 4 2 (a) Construct a probability distribution. (b) Graph the probability distribution using a histogram and describe its shape. (c) Find the mean, variance, and standard deviation of the probability distribution and interpret the results. (d) Find the probability of randomly selecting a household that has at least four computers.

Problem 1CT In Exercise, find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine whether the events are unusual. If convenient, use a table or technology to find the probabilities. One out of every 100 tax returns that a tax auditor examines requires an audit. Find the probability that (a) the first return requiring an audit is the 25th return the tax auditor examines, (b) the first return requiring an audit is the first or second return the tax auditor examines, and (c) none of the first five returns the tax auditor examines require an audit.

Problem 2CT In Exercise, find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine whether the events are unusual. If convenient, use a table or technology to find the probabilities. Twenty percent of U.S. adults have some type of mental illness. You randomly select six U.S. adults. Find the probability that the number of U.S. adults who have some type of mental illness is (a) exactly two, (b) at least one, and (c) less than three.

Problem 2E In Exercise, determine whether the random variable x is discrete or continuous. Explain your reasoning. Let x represent the weight of a truck at a weigh station.

Problem 3CQ Forty-four percent of U.S. adults believe the U.S. system of justice is fair to most Americans. You randomly select nine U.S. adults. Find the probability that the number of U.S. adults who believe the U.S. system of justice is fair to most Americans is (a) exactly three, (b) at most four, and (c) more than seven.

Problem 3E In Exercise, (a) construct a probability distribution, and (b) graph the probability distribution using a histogram and describe its shape. The number of hits per game played by Derek Jeter during a recent season Hits 0 1 2 3 4 Games 30 65 45 15 4

Problem 4CQ The success rate of corneal transplant surgery is 85%. The surgery is performed on six patients. (a) Construct a binomial distribution. (b) Graph the binomial distribution using a histogram and describe its shape. (c) Find the mean, variance, and standard deviation of the binomial distribution and interpret the results.

Problem 5CQ An online magazine finds that the mean number of typographical errors per page is five. Find the probability that the number of typographical errors found on any given page is (a) exactly five, (b) less than five, and (c) exactly zero.

Determine whether the distribution is a probability distribution. If it is not a probability distribution, explain why. ________________ Equation Transcription: Text Transcription: frac{1}{20} frac{1}{10} frac{2}{5} frac{1}{5} frac{1}{25}

Problem 3CT In Exercise, find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine whether the events are unusual. If convenient, use a table or technology to find the probabilities. The mean increase in the United States population is about four people per minute. Find the probability that the increase in the U.S. population in any given minute is (a) exactly six people, (b) more than eight people, and (c) at most four people.

Problem 5CT The table shows the ages of students in a freshman orientation course. Age 17 18 19 20 21 22 Students 2 13 4 3 2 1 (a) Construct a probability distribution. (b) Graph the probability distribution using a histogram and describe its shape. (c) Find the mean, variance, and standard deviation of the probability distribution and interpret the results. (d) Find the probability that a randomly selected student is less than 20 years old.

Problem 6CQ Basketball player Dwight Howard makes a free throw shot about 58% of the time. Find the probability that (a) the first free throw shot he makes is the fourth shot, (b) the first free throw shot he makes is the second or third shot, and (c) he does not make his first three shots.

Problem 4E In Exercise, (a) construct a probability distribution, and (b) graph the probability distribution using a histogram and describe its shape. The number of hours students in a college class slept the previous night. Hours 4 5 6 7 8 9 10 Students 1 6 13 23 14 4 2

Problem 6CT Forty-one percent of U.S. adults plan to wear green on St. Patrick’s Day. You randomly select five U.S. adults and ask them whether they plan to wear green on St. Patrick’s Day. The random variable represents the number of U.S. adults who plan to wear green on St. Patrick’s Day. (a) Construct a probability distribution. (b) Graph the probability distribution using a histogram and describe its shape. (c) Find the mean, variance, and standard deviation of the probability distribution and interpret the results.

Problem 5E In Exercise, determine whether the distribution is a probability distribution. If it is not a probability distribution, explain why. The random variable x represents the number of tickets a police officer writes out each shift. x 0 1 2 3 4 5 P(x) 0.09 0.23 0.29 0.16 0.21 0.02

Problem 7CT Determine whether the random variable x is discrete or continuous. Explain your reasoning. (a) Let x represent the length (in minutes) of a movie. (b) Let x represent the number of movies playing in a theater.

Problem 7CQ Which event(s) in Exercise can be considered unusual? Explain your reasoning. Exercise Basketball player Dwight Howard makes a free throw shot about 58% of the time. Find the probability that (a) the first free throw shot he makes is the fourth shot, (b) the first free throw shot he makes is the second or third shot, and (c) he does not make his first three shots.

In Exercises 5 and 6, determine whether the distribution is a probability distribution. If it is not a probability distribution, explain why. The random variable x represents the number of classes in which a student is enrolled in a given semester at a university. ________________ Equation Transcription: Text Transcription: frac{1}{80} frac{2}{75} frac{1}{10} frac{12}{25} frac{27}{20} frac{1}{5} frac{2}{25} frac{1}{120}

Problem 8E In Exercise, (a) find the mean, variance, and standard deviation of the probability distribution, and (b) interpret the results. A television station sells advertising in 15-, 30-, 60-, 90-, and 120-second blocks. The distribution of sales for one 24-hour day is given. Length (in seconds) 15 30 60 90 120 Probability 0.134 0.786 0.053 0.021 0.168

In Exercises 9 and 10, find the expected net gain to the player for one play of the game. A scratch-off lottery ticket costs $5. The table shows the probability of winning various prizes on the ticket. Equation Transcription: Text Transcription: frac{1}{100,000} frac{1}{100} frac{1}{50}

Problem 11E In Exercise, determine whether the experiment is a binomial experiment. If it is, identify a success, specify the values of n, p, and q, and list the possible values of the random variable x. If it is not a binomial experiment, explain why. Bags of milk chocolate M&M’s contain 24% blue candies. One candy is selected from each of 12 bags. The random variable represents the number of blue candies selected.

Problem 12E In Exercise, determine whether the experiment is a binomial experiment. If it is, identify a success, specify the values of n, p, and q, and list the possible values of the random variable x. If it is not a binomial experiment, explain why. A fair coin is tossed repeatedly until 15 heads are obtained. The random variable x counts the number of tosses.

Problem 14E In Exercise, find the indicated binomial probabilities. If convenient, use technology or Table 2 in Appendix B to find the probabilities. Thirty-four percent of U.S. adults personally own a gun. You randomly select 12 U.S. adults. Find the probability that the number of U.S. adults who say they personally own a gun is (a) exactly two, (b) at least two, and (c) more than two.

Problem 13E In Exercise, find the indicated binomial probabilities. If convenient, use technology or Table 2 in Appendix B to find the probabilities. About 30% of U.S. adults are trying to lose weight. You randomly select eight U.S. adults. Find the probability that the number of U.S. adults who say they are trying to lose weight is (a) exactly three, (b) at least three, and (c) more than three.

Problem 17E In Exercise, (a) construct a binomial distribution, (b) graph the binomial distribution using a histogram and describe its shape, and (c) identify any values of the random variable x that you would consider unusual. Explain your reasoning. Thirty-eight percent of employed wives in the United States earn more than their husbands. You randomly select five employed U.S. wives and ask them whether they earn more than their husbands. The random variable represents the number of employed U.S. wives who earn more than their husbands.

Problem 15E In Exercise, find the indicated binomial probabilities. If convenient, use technology or Table 2 in Appendix B to find the probabilities. Forty-three percent of businesses in the United States require a doctor’s note when an employee takes sick time. You randomly select nine businesses. Find the probability that the number of businesses who say they require a doctor’s note when an employee takes sick time is (a) exactly five, (b) at least five, and (c) more than five.

Problem 19E In Exercise, find the (a) mean, (b) variance, and (c) standard deviation of the binomial distribution for the given random variable, and (d) interpret the results. About 14% of U.S. drivers are uninsured. You randomly select eight U.S. drivers and ask them whether they are uninsured. The random variable represents the number of U.S. drivers who are uninsured.

Problem 18E In Exercise, (a) construct a binomial distribution, (b) graph the binomial distribution using a histogram and describe its shape, and (c) identify any values of the random variable x that you would consider unusual. Explain your reasoning. About 56% of U.S. high school students participate in athletics. You randomly select six U.S. high school students and ask them whether they participate in athletics. The random variable represents the number of U.S. high school students who participate in athletics.

Problem 16E In Exercise, find the indicated binomial probabilities. If convenient, use technology or Table 2 in Appendix B to find the probabilities. In a typical day, 61% of U.S. adults go online to get news. You randomly select five U.S. adults. Find the probability that the number of U.S. adults who say they go online to get news is (a) exactly two, (b) at least two, and (c) more than two.

Problem 20E In Exercise, find the (a) mean, (b) variance, and (c) standard deviation of the binomial distribution for the given random variable, and (d) interpret the results. Sixty-three percent of U.S. mothers with school-age children choose fast food as a dining option for their families one to three times a week. You randomly select five U.S. mothers with school-age children and ask whether they choose fast food as a dining option for their families one to three times a week. The random variable represents the number of U.S. mothers who choose fast food as a dining option for their families one to three times a week.

Problem 21E Twenty-two percent of former smokers say they tried to quit four or more times before they were habit-free. You randomly select 10 former smokers. Find the probability that the first person who tried to quit four or more times is (a) the third person selected, (b) the fourth or fifth person selected, and (c) not one of the first seven people selected.

Problem 23E Thirty-seven percent of U.S. adults think the practice of changing their clocks for Daylight Savings Time (DST) is worth the hassle. You randomly select seven U.S. adults. Find the probability that the number of U.S. adults who say changing their clocks for DST is worth the hassle is (a) exactly four, (b) less than two, and (c) at least six.

Problem 22E During a 73-year period, tornadoes killed about 0.28 people per day in the United States. Assume this rate holds true today and is constant throughout the year. Find the probability that the number of people in the United States killed by a tornado tomorrow is (a) exactly zero, (b) at most two, and (c) more than one.

Problem 24E In a recent season, hockey player Evgeni Malkin scored 50 goals in 75 games he played. Assume that his goal production stayed at that level for the next season. Find the probability that he would get his first goal (a) in the first game of the season, (b) in the second game of the season, and (c) within the first three games of the season.

Problem 7E In Exercise, (a) find the mean, variance, and standard deviation of the probability distribution, and (b) interpret the results. The number of cell phones per household in a small town Cell phones 0 1 2 3 4 5 6 Probability 0.020 0.140 0.272 0.292 0.168 0.076 0.032

Problem 9E In Exercise, find the expected net gain to the player for one play of the game. It costs $25 to bet on a horse race. The horse has a 1/8 chance of winning and a ¼ chance of placing 2nd or 3rd. You win $125 if the horse wins and receive your money back if the horse places 2nd or 3rd.