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mathematics
statistics
Fundamentals Of Statistics 4th Edition Michael Sullivan III - Solutions
Determine whether the probability experiment represents a binomial experiment. If not, explain why. (a) According to the Chronicle of Higher Education, there is a 54% probability that a randomly selected incoming freshman will graduate from college within 6 years. Suppose that 10 incoming freshmen
The probability that a randomly selected patient who visits the emergency room (ER) will die within 1 year of the visit is 0.05.(a) What is the probability that exactly 1 of 10 randomly selected visitors to the ER will die within 1 year? Interpret this result.(b) What is the probability that fewer
According to a Gallup poll, 60% of U.S. women 18 years old or older stated that the minimum driving age should be 18. In a random sample of 15 U.S. women 18 years old or older, find the probability that: (a) Exactly 10 believe that the minimum driving age should be 18. (b) Fewer than 5 believe
Consider a binomial probability distribution with parameters n = 8 and p = 0.75.(a) Construct a binomial probability distribution with these parameters.(b) Compute the mean and standard deviation of the distribution. (c) Draw the probability histogram, comment on its shape, and label the mean on
In sampling without replacement, the assumption of independence required for a binomial experiment is violated. Under what circumstances can we sample without replacement and still use the binomial probability formula to approximate probabilities?
According to the article “Self-injurious Behaviors in a College Population,” 17% of undergraduate or graduate students have had at least one incidence of self-injurious behavior. The researchers conducted a survey of 40 college students who reported a history of emotional abuse and found that
Determine whether the random variable is discrete or continuous. In each case, state the possible values of the random variable. (a) The number of days with measurable rainfall in Honolulu, Hawaii, during a year (b) The miles per gallon of gasoline obtained by a randomly selected Toyota Prius (c)
Determine whether the distribution is a discrete probability distribution. If not, state why. (a) x .... P(x) 0 .... 0.324 1 .... 0.121 2 .... 0.247 3 .... 0.206 4 .... 0.102 (b) x .... P(x) 0 .... 0.34 1 .... 0.28 2 .... 0.26 3 .... 0.23 4 .... −0.11
At the Wimbledon Tennis Championship, to win a match in men’s singles a player must win the best of five sets. The following data represent the number of sets played, X, in the men’s singles final match for the years 1968 to 2011.x ....Frequency3 ....194 ....125 ....13(a) Construct a
A life insurance company sells a $100,000 one-year term life insurance policy to a 35-year-old male for $200. According to the National Vital Statistics Report, 56(9), the probability the male survives the year is 0.998725. Compute and interpret the expected value of this policy to the life
State the criteria that must be met for an experiment to be a binomial experiment.
Determine whether the probability experiment represents a binomial experiment. If not, explain why. (a) An urn contains 20 colored golf balls: 8 white, 6 red, 4 blue, and 2 yellow. A child is allowed to draw balls until he gets a yellow one. The number of draws required is recorded. (b) According
Suppose the adult American population is equally split in their belief that the amount of tax (federal, state, property, sales, and so on) they pay is too high. (a) How many people would we expect to say they pay too much tax if we surveyed 1200 randomly selected adult Americans? (b) Explain why we
Consider a binomial probability distribution with parameters n = 5 and p = 0.2.(a) Construct a binomial probability distribution with these parameters.(b) Compute the mean and standard deviation of the distribution. (c) Draw the probability histogram, comment on its shape, and label the mean on the
What is the difference between a discrete random variable and a continuous random variable? Provide your own examples of each.
Determine whether the random variable is discrete or continuous. In each case, state the possible values of the random variable. (a) The number of light bulbs that burn out in the next week in a room with 20 bulbs. (b) The time it takes to fly from New York City to Los Angeles. (c) The number of
Determine whether the random variable is discrete or continuous. In each case, state the possible values of the random variable. (a) The time it takes for a light bulb to burn out. (b) The weight of a T-bone steak. (c) The number of free-throw attempts before the first shot is made. (d) In a
Determine whether the random variable is discrete or continuous. In each case, state the possible values of the random variable. (a) The amount of rain in Seattle during April. (b) The number of fish caught during a fishing tournament. (c) The number of customers arriving at a bank between noon
Determine whether the random variable is discrete or continuous. In each case, state the possible values of the random variable. (a) The number of defects in a roll of carpet. (b) The distance a baseball travels in the air after being hit. (c) The number of points scored during a basketball
Determine whether the distribution is a discrete probability distribution. If not, state why. x .... P(x) 0 .... 0.2 1 .... 0.2 2 .... 0.2 3 .... 0.2 4 .... 0.2
Determine whether the distribution is a discrete probability distribution. If not, state why. x .... P(x) 0 .... 0.1 1 .... 0.5 2 .... 0.05 3 .... 0.25 4 .... 0.1
Determine whether the distribution is a discrete probability distribution. If not, state why. x .... P(x) 1 .... 0 2 .... 0 3 .... 0 4 .... 0 5 .... 1
Determine the required value of the missing probability to make the distribution a discrete probability distribution. x .... P(x) 3 .... 0.4 4 .... ? 5 .... 0.1 6 .... 0.2
Determine the required value of the missing probability to make the distribution a discrete probability distribution. x .... P(x) 0 .... 0.30 1 .... 0.15 2 .... ? 3 .... 0.20 4 .... 0.15 5 .... 0.05
In the Sullivan Statistics Survey, individuals were asked to disclose the number of televisions in their household. In the following probability distribution, the random variable X represents the number of televisions in households. Number of Televisions, x .... P(x) 0 ............. 0 1
In the following probability distribution, the random variable X represents the number of activities a parent of a 6th- to 8th-grade student is involved in. x .... P(x) 0 .... 0.073 1 .... 0.117 2 .... 0.258 3 .... 0.322 4 .... 0.230 (a) Verify that this is a discrete probability distribution. (b)
In the 2004 baseball season, Ichiro Suzuki of the Seattle Mariners set the record for the most hits in a season with a total of 262 hits. In the following probability distribution, the random variable X represents the number of hits Ichiro obtained in a game. x .... P(x) 0 .... 0.1677 1
A Wendy’s manager performed a study to determine a probability distribution for the number of people, X, waiting in line during lunch. The results were as follows: x .... P(x) 0 .... 0.011 1 .... 0.035 2 .... 0.089 3 .... 0.150 4 .... 0.186 5 .... 0.172 6 .... 0.132 7 .... 0.098 8 .... 0.063 9
The following data represent the number of games played in each World Series from 1923 to 2010.(a) Construct a discrete probability distribution for the random variable X,(b) Draw the probability histogram,(c) Compute and interpret the mean of the random variable X, and(d) Compute the standard
What is the ideal number of children to have in a family? The following data represent the ideal number of children for a random sample of 900 adult Americans.(a) Construct a discrete probability distribution for the random variable X,(b) Draw the probability histogram,(c) Compute and interpret the
Toss is a popular application for smart phones. The goal of the game is to toss crumbled paper into a trash can while accounting for wind from a fan. The following data represent the ratings (on a scale from 1 to 5) with 1 representing a poor rating.(a) Construct a discrete probability distribution
The following data, obtained from the Sullivan Statistics Survey, represent the number of speeding tickets individuals received in the past 12 months.(a) Construct a discrete probability distribution for the random variable X,(b) Draw the probability histogram,(c) Compute and interpret the mean of
The probability histogram on the following page represents the number of live births by a mother 50 to 54 years old who had a live birth in 2007.(a) What is the probability that a randomly selected 50- to 54-year-old mother who had a live birth in 2007 has had her fourth live birth? (b) What is the
The probability histogram represents the number of rooms in rented housing units in 2009.(a) What is the probability that a randomly selected rental unit has ï¬ve rooms? (b) What is the probability that a randomly selected rental unit has ï¬ve or six rooms? (c) What is
A life insurance company sells a $250,000 1-year term life insurance policy to a 20-year-old female for $200. According to the National Vital Statistics Report, 58(21), the probability that the female survives the year is 0.999544. Compute and interpret the expected value of this policy to the
A life insurance company sells a $250,000 1-year term life insurance policy to a 20-year-old male for $350. According to the National Vital Statistics Report, 58(21), the probability that the male survives the year is 0.998734. Compute and interpret the expected value of this policy to the
An investment counselor calls with a hot stock tip. He believes that if the economy remains strong, the investment will result in a profit of $50,000. If the economy grows at a moderate pace, the investment will result in a profit of $10,000. However, if the economy goes into recession, the
Shawn and Maddie purchase a foreclosed property for $50,000 and spend an additional $27,000 fixing up the property. They feel that they can resell the property for $120,000 with probability 0.15, $100,000 with probability 0.45, $80,000 with probability 0.25, and $60,000 with probability 0.15.
In the game of roulette, a player can place a $5 bet on the number 17 and have a 1/38 probability of winning. If the metal ball lands on 17, the player wins $175. Otherwise, the casino takes the player’s $5. What is the expected value of the game to the player? If you played the game 1000 times,
In the Cash Five Lottery in Connecticut, a player pays $1 for a single ticket with five numbers. Five balls numbered 1 through 35 are randomly chosen from a bin without replacement. If all five numbers on a player’s ticket match the five chosen, the player wins $100,000. The probability of
Powerball is a multistate lottery. The following probability distribution represents the cash prizes of Powerball with their corresponding probabilities.x (cash prize, $) ...........P(x)Grand prize ...........0.00000000684200,000 ........... 0.0000002810,000 ............. 0.000001711100
Some standardized tests, such as the SAT test, incorporate a penalty for wrong answers. For example, a multiple-choice question with five possible answers will have 1 point awarded for a correct answer and 1 4 point deducted for an incorrect answer. Questions left blank are worth 0 points. (a)
One question from the Sullivan Statistics Survey was “How many credit cards do you currently have?” This question was asked of only those individuals who have a credit card. Answer the following questions based on the results of the survey.(a) Determine the mean number of credit cards based on
An experimental drug is administered to 100 randomly selected individuals, with the number of individuals responding favorably recorded.
A poll of 1200 registered voters is conducted in which the respondents are asked whether they believe Congress should reform Social Security.
Three cards are selected from a standard 52-card deck without replacement. The number of aces selected is recorded.
Three cards are selected from a standard 52-card deck with replacement. The number of kings selected is recorded.
One hundred randomly selected U.S. parents with at least one child under the age of 18 are surveyed and asked if they have ever spanked their child. The number of parents who have spanked their child is recorded.
In a town with 400 citizens, 100 randomly selected citizens are asked to identify their religion. The number who identify with a Christian religion is recorded.
A binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment. n = 10, p = 0.4, x = 3
A binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment. n = 15, p = 0.85, x = 12
A binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment. n = 40, p = 0.99, x = 38
A binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment. n = 50, p = 0.02, x = 3
A binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment. n = 8, p = 0.35, x = 3
A binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment. n = 20, p = 0.6, x = 17
A binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment. n = 9, p = 0.2, x ≤ 3
A binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment. n = 10, p = 0.65, x < 5
A binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment. n = 7, p = 0.5, x > 3
A binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment. n = 20, p = 0.7, x ≥ 12
A binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment. n = 12, p = 0.35, x ≤ 4
A binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment. n = 11, p = 0.75, x ≥ 8
n = 6, p = 0.3(a) Construct a binomial probability distribution with the given parameters;(b) Compute the mean and standard deviation of the random variable using the methods of Section 6.1;(c) Compute the mean and standard deviation, using the methods of this section; and(d) Draw the probability
n = 8, p = 0.5(a) Construct a binomial probability distribution with the given parameters;(b) Compute the mean and standard deviation of the random variable using the methods of Section 6.1;(c) Compute the mean and standard deviation, using the methods of this section; and(d) Draw the probability
n = 9, p = 0.75(a) Construct a binomial probability distribution with the given parameters;(b) Compute the mean and standard deviation of the random variable using the methods of Section 6.1;(c) Compute the mean and standard deviation, using the methods of this section; and(d) Draw the probability
n = 10, p = 0.2(a) Construct a binomial probability distribution with the given parameters;(b) Compute the mean and standard deviation of the random variable using the methods of Section 6.1;(c) Compute the mean and standard deviation, using the methods of this section; and(d) Draw the probability
n = 10, p = 0.5(a) Construct a binomial probability distribution with the given parameters;(b) Compute the mean and standard deviation of the random variable using the methods of Section 6.1;(c) Compute the mean and standard deviation, using the methods of this section; and(d) Draw the probability
n = 9, p = 0.8(a) Construct a binomial probability distribution with the given parameters;(b) Compute the mean and standard deviation of the random variable using the methods of Section 6.1;(c) Compute the mean and standard deviation, using the methods of this section; and(d) Draw the probability
According to flightstats.com, American Airlines flights from Dallas to Chicago are on time 80% of the time. Suppose 15 flights are randomly selected, and the number of on-time flights is recorded. (a) Explain why this is a binomial experiment. (b) Find and interpret the probability that exactly
According to the American Lung Association, 90% of adult smokers started smoking before turning 21 years old. Ten smokers 21 years old or older are randomly selected, and the number of smokers who started smoking before 21 is recorded. (a) Explain why this is a binomial experiment. (b) Find and
In a recent poll, the Gallup Organization found that 45% of adult Americans believe that the overall state of moral values in the United States is poor. Suppose a survey of a random sample of 25 adult Americans is conducted in which they are asked to disclose their feelings on the overall state of
Clarinex-D is a medication whose purpose is to reduce the symptoms associated with a variety of allergies. In clinical trials of Clarinex-D, 5% of the patients in the study experienced insomnia as a side effect. A random sample of 20 Clarinex-D users is obtained, and the number of patients who
According to a study done by Nick Wilson of Otago University Wellington, the probability a randomly selected individual will not cover his or her mouth when sneezing is 0.267. Suppose you sit on a bench in a mall and observe people’s habits as they sneeze. (a) What is the probability that among
According to a study done by Nick Wilson of Otago University Wellington, the probability a randomly selected individual will cover his or her mouth with a tissue, handkerchief, or elbow (the method recommended by public health officials) is 0.047. Suppose you sit on a bench in a mall and observe
Twelve jurors are randomly selected from a population of 3 million residents. Of these 3 million residents, it is known that 45% are Hispanic. Of the 12 jurors selected, 2 are Hispanic. (a) What proportion of the jury described is Hispanic? (b) If 12 jurors are randomly selected from a population
According to paint manufacturer DuPont, 6% of all cars worldwide are red. In the Sullivan Statistics Survey, of 175 respondents, 17, or 9.7%, indicated the color of their car is red. Determine if the results of the Sullivan Survey contradict those of DuPont by computing P(X ≥ 17), where X is a
According to flightstats.com, American Airlines flights from Dallas to Chicago are on time 80% of the time. Suppose 100 flights are randomly selected. (a) Compute the mean and standard deviation of the random variable X, the number of on-time flights in 100 trials of the probability experiment. (b)
According to the American Lung Association, 90% of adult smokers started smoking before turning 21 years old. (a) Compute the mean and standard deviation of the random variable X, the number of smokers who started before turning 21 years old in 200 trials of the probability experiment. (b)
In a recent poll, the Gallup Organization found that 45% of adult Americans believe that the overall state of moral values in the United States is poor. (a) Compute the mean and standard deviation of the random variable X, the number of adults who believe that the overall state of moral values in
Clarinex-D is a medication whose purpose is to reduce the symptoms associated with a variety of allergies. In clinical trials of Clarinex-D, 5% of the patients in the study experienced insomnia as a side effect. (a) If 240 users of Clarinex-D are randomly selected, how many would we expect to
In March 1995, The Harris Poll reported that 80% of parents spank their children. Suppose a recent poll of 1030 adult Americans with children finds that 781 indicated that they spank their children. If we assume parents’ attitude toward spanking has not changed since 1995, how many of 1030
In May, 2000, the Gallup Organization reported that 11% of adult Americans had a great deal of trust and confidence in the federal government handling domestic issues. Suppose a survey of a random sample of 1100 adult Americans finds that 84 have a great deal of trust and confidence in the
In August 2007, Google™ accounted for 53.6% of all U.S. Internet searches. Assuming this percentage is still accurate today, would it be unusual to observe 600 searches using Google™ in a random sample of 1000 U.S. Internet searches? Why?
Singulair is a medication whose purpose is to control asthma attacks. In clinical trials of Singulair, 18.4% of the patients in the study experienced headaches as a side effect. Would it be unusual to observe 86 patients who experience headaches in a random sample of 400 patients who use this
The following excerpt is from the Racial Profiling Data Collection Resource Center (www.racialprofilinganalysis.neu.edu/). In 2006, the New York City Police Department stopped a half-million pedestrians for suspected criminal involvement. Raw statistics for these encounters suggest large racial
According to the U.S. National Center for Health Statistics, there is a 98% probability that a 20-year-old male will survive to age 30.(a) Using statistical software, simulate taking 100 random samples of size 30 from this population.(b) Using the results of the simulation, compute the probability
According to the High School Athletics Participation Survey, approximately 55% of students enrolled in high schools participate in athletic programs. You are performing a study of high school students and would like at least 11 students in the study to be participating in athletics. (a) How many
According to the 2008 American Community Survey, 27% of residents of the United States 25 years old or older had earned at least a bachelor’s degree. You are performing a study and would like at least 10 people in the study to have earned at least a bachelor’s degree. (a) How many residents of
State the criteria for a binomial probability experiment.
Explain how the value of p, the probability of success, affects the shape of the binomial probability histogram.
When can the Empirical Rule be used to identify unusual results in a binomial experiment? Why can the Empirical Rule be used to identify results in a binomial experiment?
Use the ï¬gure to answer the questions that follow.(a) What is µ? (b) What is σ? (c) Suppose that the area under the normal curve to the right of x = 75 is 0.0668. Provide two interpretations for this area. (d) Suppose that the area under the normal curve between x =
The area to the left of z = -1.04. Draw a standard normal curve and shade the area indicated. Then find the area of the shaded region.
The area between z = -0.34 and z = 1.03. Draw a standard normal curve and shade the area indicated. Then find the area of the shaded region.
Find the z-score such that the area to the right of the z-score is 0.483.
Find the z-scores that separate the middle 92% of the data from the area in the tails of the standard normal distribution.
Find the value of z0.20.
Draw the normal curve with the parameters indicated. Then find the probability of the random variable X. Shade the area that represents the probability. µ = 50, σ = 6, P(X > 55)
Draw the normal curve with the parameters indicated. Then find the probability of the random variable X. Shade the area that represents the probability. µ = 30, σ = 5, P(X ≤ 23)
Draw the normal curve with the parameters indicated. Then find the probability of the random variable X. Shade the area that represents the probability. µ = 70, σ = 10, P(65 < X < 85)
Suppose that Dunlop Tire manufactures a tire with a lifetime that approximately follows a normal distribution with mean 70,000 miles and standard deviation 4400 miles. (a) What proportion of the tires will last at least 75,000 miles? (b) Suppose that Dunlop warrants the tires for 60,000 miles. What
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