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Mind On Statistics 4th Edition David D Busch, Jessica M Utts, Robert F Heckard - Solutions

Annmarie is trying to decide whether to take the train or the bus into the city. The train takes longer but is more predictable than the bus because there are no traffic delays.Train times are approximately normally distributed, with mean 5 60 minutes and standard deviation 5 2 minutes, while bus
Charles, Julia, and Alex are in grades 4, 3, and 2, respectively, and are representing their school at a spelling bee.The school’s team score is the sum of the number of words the individual students spell correctly out of 50 words each.Different words are given for each grade level. From
Joe performs remarkably well on remote viewing ESP tests, which require the “viewer” to draw a picture, and then determine which of four possible photos was the intended“target.” Because the target is randomly selected from among the four choices, the probability of a correct match by
Ethan has a midterm in his statistics class, which starts 10 minutes after the scheduled end of his biology class. The biology teacher rarely ends class on time though, and the amount of time he is overtime is approximately normally distributed, with a mean of 2 minutes and a standard deviation of
Give the mean, variance, and standard deviation of the sum X 1 Y in each of the following cases. You can assume X and Y are independent. For any situation(s)covered in Section 8.8, name what distribution the sum X 1 Y has.a. X is a binomial random variable with n 5 10, p 5 .5.Y is a binomial random
The variable X has a normal distribution with mean μ 5 75 and standard deviation s 5 6. The variable Y has a normal distribution with mean μ 5 70 and standard deviation s 5 8. Variables X and Y are independent.a. Find the mean and standard deviation of the sum X 1 Y.b. Find the mean and standard
Isabelle and Taylor work together on a group quiz that has 15 multiple-choice questions, each with four choices for the possible answer. Unfortunately, neither had time to study, so they decide to randomly guess at all answers. Isabelle guesses answers for the first 7 questions, and Taylor guesses
inches. Two unrelated men will be randomly sampled. Let X 5 height of the first man and Y 5 height of the second man.a. Consider D 5 X 2 Y, the difference between the heights of the two men. What type of distribution will the variable D have?b. What is the mean value for the distribution of D?c.
Suppose the heights of adult males in a population have a normal distribution with mean μ 5 70 inches and standard deviation s 5
Suppose the length of time a person takes to use an ATM machine is normally distributed with mean μ 5 100 seconds and standard deviation s 5 10 seconds. There are n 5 4 people ahead of Jackson in a line of people waiting to use the machine. He is concerned about T 5 total time the four people will
In a test for extrasensory perception, the participant repeatedly guesses the suit of a card randomly sampled with replacement from an ordinary deck of cards. There are four suits, all equally likely. The participant guesses 100 times, and X 5 number of correct guesses.a. Explain why X is a
An allergy medication is successful for 70% of all patients who use it. The medication is given to 200 patients. Let X 5 number of successful treatments.a. What are the mean and standard deviation of X?b. Use the normal curve to approximate the probability that X is 128 or less.
To be eligible for a certain job, women must be at least 62 inches tall, and 87% of women meet this criterion. In a random sample of 2000 women, X 5 number who qualify for the job (based on height).a. Use the normal curve to approximate P(X # 1700), the probability that 1700 or fewer women have the
A random sample of 1000 eligible voters is drawn, and X 5 number who actually voted in the last election. It is known that 60% of all eligible voters did vote.a. Use the normal approximation to the binomial distribution to approximate P(X # 620), the probability that 620 or fewer individuals in the
Suppose that a fair coin is flipped n 5 100 times.a. Calculate the mean and standard deviation of X 5 number of heads. (Hint: The variable X has a binomial distribution.)b. Use the normal approximation to the binomial distribution to estimate the probability that the number of heads is greater than
Suppose that p 5 .512 is the proportion of one-child families in which the child is a boy.a. For a random sample of n 5 50 one-child families, use the normal approximation to the binomial distribution to estimate the probability that there will be 20 or fewer families with one boyb. Repeat part (a)
Refer to Exercises 8.78 and 8.79. Find the height such that about 10% of college women are taller than that height.What is the percentile ranking for that height?
Refer to Exercise 8.78. Find the height such that about 25% of college women are shorter than that height. What is the percentile ranking for that height?
Heights for college women are normally distributed with mean 5 65 inches and standard deviation 5 2.7 inches.Find the proportion of college women whose heights fall into the following ranges:a. Between 62 inches and 65 inches.b. Between 60 inches and 70 inches.c. Less than 70 inches.d. Greater than
Find the value z* that satisfies each of the following probabilities for a standard normal random variable Z:a. P(Z # z*) 5 .025.b. P(Z # z*) 5 .975.c. P(2z* # Z # z *) 5 .95.
Refer to Exercise 8.75. Suppose that in a given year, the total rainfall is only 6 inches. You work for the local newspaper, and your editor has asked you to write a story about the terrible drought the town is suffering and how abnormal the situation is. Write a few sentences that you could use to
Suppose the yearly rainfall totals for a city in northern California follow a normal distribution, with a mean of 18 inches and a standard deviation of 6 inches. For a randomly selected year, what is the probability that total rainfall will be in each of the following intervals?a. Less than 10
Find the following probabilities for a standard normal random variable Z:a. P(Z # 23.72).b. P(23.72 # Z # 3.72).c. P(Z $ 1.5).d. P(Z . 20.67)b. What is the probability that a randomly selected student spends more than $240 on textbooks this semester?c. What is the probability that a randomly
Find the following probabilities for a standard normal random variable Z:a. P(Z # 21.4).b. P(Z # 1.4).c. P(21.4 # Z # 1.4).d. P(Z $ 1.4).
Draw the density curve corresponding to each of the following normal random variables, and then shade the area corresponding to the desired probability. You do not need to compute the probability.a. X is a normal random variable with μ 5 75 and s 5 5, P(70 # X # 85).b. X is a normal random
Weights (X) of men in a certain age group have a normal distribution with mean μ 5 180 pounds and standard deviation s 5 20 pounds. Find each of the following probabilities:a. P(X # 200) 5 probability the weight of a randomly selected man is less than or equal to 200 pounds.b. P(X # 165) 5
For each value of z*, find the cumulative probability P(Z # z*):a. z* 5 1.96.b. z* 5 22.33.c. z* 5 2.58.d. z* 5 1.65.
For each value of z*, find the cumulative probability P(Z # z*):a. z* 5 0.b. z* 5 20.35.c. z* 5 0.35.
In each situation below, calculate the standardized score(or z-score) for the value x:a. Mean μ 5 65, standard deviation s 5 4, value x 5 70.b. Mean μ 5 120, standard deviation s 5 10, value x 5 115.c. Mean μ 5 72, standard deviation s 5 8, value x 5 82.d. Mean μ 5 72, standard deviation s 5 8,
In each situation below, calculate the standardized score(or z-score) for the value x:a. Mean μ 5 0, standard deviation s 5 1, value x 5 1.5.b. Mean μ 5 10, standard deviation s 5 6, value x 5 4.c. Mean μ 5 10, standard deviation s 5 5, value x 5 0.d. Mean μ 5 210, standard deviation s 5 15,
Find the probabilities specified in each of the parts of Exercise 8.60.
Give an example of a uniform random variable that might occur in your daily life.
Draw the density curve corresponding to each of the following random variables, and then shade the area corresponding to the desired probability. You do not need to compute the probability.a. X is a uniform random variable from 10 to 20, P(10 # X # 13).b. X is a uniform random variable from 0 to
A game is played with a spinner on a circle, like the minute hand on a clock. The circle is marked evenly from 0 to 100, so, for example, the 3:00 position corresponds to 25, the 6:00 position to 50, and so on. The player spins the spinner,and the resulting number is the number of seconds he or she
Suppose that the time students wait for a bus can be described by a uniform random variable X, where X is between 0 minutes and 60 minutes.a. What is the probability that a student will wait between 0 and 30 minutes for the next bus?b. What is the probability that a student will have to wait at
Suppose that X is a uniform random variable where X is between 0 and 10.a. What is the probability that X will be between 0 and 3?b. What is the probability that X will be between 4 and 8?c. What is the probability that X will be between 5 and 10?
A computer is used to generate n 5 6 random integers, each between 0 and 9 (with replacement). X 5 the number of even numbers among the six numbers picked. Find probabilities for the following events.a. Three even numbers are picked.b. Four or fewer even numbers are picked.c. More than four even
For each of the following scenarios, write the desired probability in a format such as P(X 5 10) and specify n and p. Do not actually compute the desired probability. If you cannot specify a numerical value for p, write in words what it represents.a. A random sample of 1000 adults is drawn from the
For each of the following situations, assume that X is a binomial random variable with the specified n and p, and find the requested probability.a. n 5 10, p 5 .3, P(X # 3).b. n 5 5, p 5 .1, P(X 5 0).c. n 5 5, p 5 .1, P(X $ 1).
For each of the following situations, assume that X is a binomial random variable with the specified n and p, and find the requested probability.a. n 5 10, p 5 .5, P(X 5 4).b. n 5 10, p 5 .3, P(X $ 4).
In an ESP test, a “participant” tries to draw a hidden “target”photograph that is unknown to anyone in the room. After the drawing attempt, the participant is shown four choices and asked to determine which one had been the real target.The real target is randomly selected from the four
Suppose that in a very large population, 10% of individuals are left-handed. Five individuals will be sampled.X 5 number of left-handed individuals among these five people. Find probabilities for the following events.a. Exactly one of the five individuals is left-handed.b. At most one of the five
A computer chess game and a human chess champion are evenly matched. They play ten games. Find probabilities for the following events.a. They each win five games.b. The computer wins seven games.c. The human chess champion wins at least seven games.
Explain which of the conditions for a binomial experiment is not met for each of the following random variables:a. A football team plays 12 games in its regular season.X 5 number of games the team wins.b. A woman buys a lottery ticket every week for which the probability of winning anything at all
Assuming that X is a binomial random variable with n 5 4 and p 5 .7, find the probability for each of the following values of X.a. X 5 2.b. X 5 0.c. X 5 1.
Find the expected value and standard deviation for a binomial random variable with each of the following values of n and p:a. n 5 10, p 5 1/2.b. n 5 100, p 5 1/4.c. n 5 2500, p 5 1/5.d. n 5 1, p 5 1/10.e. n 5 30, p 5 .4.
Find the mean and standard deviation for a binomial random variable X with each of the following values of n and p:a. n 5 10, p 5 .50.b. n 5 1, p 5 .40.c. n 5 100, p 5 .90.d. n 5 30, p 5 .01.
Assuming that X is a binomial random variable with n 5 10 and p 5 .20, find the probability for each of the following values of X:a. X 5 5.b. X 5 2.c. X 5 1.d. X 5 9.
Refer to Exercise 8.43. Find μ in each case.
For each of the following binomial random variables, specify n and p:a. A fair die is rolled 30 times. X 5 number of times a 6 is rolled.b. A company puts a game card in each box of cereal and 1/100 of them are winners. You buy ten boxes of cereal, and X 5 number of times you win.c. Jack likes to
For each of the examples below, decide if X is a binomial random variable. If so, specify n and p. If not, explain why not.a. X 5 number of heads from flipping the same coin ten times, where the probability of a head 5 1/2.b. X 5 number of heads from flipping two coins five times each, where the
A fair coin is flipped 200 times. The random variable X 5 number of heads out of the 200 tosses.a. Is X a binomial random variable? If so, specify n and p.If not, explain why not.b. What is the expected value of X?
Suppose you have to cross a train track on your commute.The probability that you will have to wait for a train is 1/5, or.20. If you don’t have to wait, the commute takes 15 minutes, but if you have to wait, it takes 20 minutes.a. What is the expected value of the time it takes you to commute?b.
In 2004, 70% of children in the United States were living with both parents, 23% were living with mother only, 3% were living with father only, and 4% were not living with either parent(http://www.census.gov/prod/2008pubs/p70-114.pdf, p. 4).a. What is the expected value for the number of parents
Refer to Exercise 8.37. If the insurance company wants to make a net profit of $10 per policyholder for the year, how much should it charge each person for insurance? Ignore administrative and other costs.
An insurance company expects 10% of its policyholders to collect claims of $500 this year and the remaining 90% to collect no claims. What is the expected value for the amount they will pay out in claims per person?
Suppose the probability that you get an A in any class you take is .3 and the probability that you get a B is .7. To construct a grade point average, an A is worth 4.0 and a B is worth 3.0.a. What is the expected value for your grade point average?b. Would you expect to have this grade point
Find the standard deviation for the net gain in the California Decco lottery game in Example 8.1 (p. 272).
Find the standard deviation for the sum of two fair dice. The probability distribution was found in Example 8.10 (p. 270).
(p. 267).
Find the expected value for the number of girls in a family with three children, assuming that boys and girls are equally likely. Use the probability distribution function given in Example
Find the expected value for the sum of two fair dice. The probability distribution function was found in Example 8.10(p. 270).
A random variable X has the following probability distribution:X 22 0 2 Probability .25 .50 .25a. Calculate the mean of X.b. Calculate the variance of X.c. Calculate the standard deviation of X.
A random variable X has the following probability distribution:X 21 0 1 Probability .25 .50 .25a. Calculate the mean of X.b. Calculate the variance of X.c. Calculate the standard deviation of X.
Exercise 8.16 gave the following table for the probability distribution of X 5 number of wins in three independent plays of a game for which the chance of winning each game 5 .2.X 5 Number of wins 0123 Probability .512 .384 .096 .008a. What is the expected value of X?b. Write a sentence that
Exercise 8.11 gave the following distribution for X 5 the number of meals eaten yesterday by individuals in a large population:Meals, X 1234 Probability .10 .32 .56 .02a. Calculate the expected value of X.b. Write a sentence that interprets the expected value of X in this situation.
The probability that Mary will win a game is .01, so the probability that she will not win is .99. If Mary wins, she will be given $100; if she loses, she must pay $5. If X 5 amount of money Mary wins (or loses), what is the expected value of X?
The Brann family wants to be financially prepared to have children. A financial advisor informs them that on the basis of families with similar characteristics, the probability distribution for the random variable X 5 number of children they might have is as follows:No. of Children 0123 Probability
Suppose that in a gambling game, the probability of winning$4 is .3 and the probability of losing $2 is .7.a. Write a table that gives the probability distribution for X 5 amount won in a single play. Losing $2 can be expressed as “winning” 2$2.b. Calculate the expected value of X 5 amount won
Explain which would be of more interest in each of the following situations—the probability distribution function or the cumulative probability distribution function for X. If you think both would be of interest, explain why.a. A pharmaceutical company wants to show that its new drug is effective
Explain which would be of more interest in each of the following situations, the probability distribution function or the cumulative probability distribution function for X. If you think both would be of interest, explain why.a. A politician wants to know how her constituents feel about a proposed
Refer to Example 8.10 (p. 270). Find the cumulative distribution function (cdf) for the sum of two fair dice.
A woman decides to have children until she has her first girl or until she has four children, whichever comes first. Let X 5 number of children she has. For simplicity, assume that the probability of a girl is .5 for each birth.a. Write the simple events in the sample space. Use B for boy and G for
Consider three tosses of a fair coin. Write the sample space, and then find the probability distribution function for each of the following random variables:a. X 5 number of tails.b. Y 5 the difference between the number of heads and the number of tails.
Let the random variable X 5 number of phone calls you will get in the next 24 hours. Suppose the possible values for X are 0, 1, 2, or 3, and their probabilities are .1, .1, .3, and .5, respectively. For instance, the probability that you will receive no calls is .1.a. Verify that the “Conditions
A kindergarten class has three left-handed children and seven right-handed children. Two children are selected without replacement for a shoe-tying lesson. Let X 5 the number who are left-handed.a. Write the simple events in the sample space. For instance, one simple event is RL, indicating that
Refer to Example 8.10 (p. 270), in which the probability distribution is given for the sum of two fair dice. Use the distribution to find the probability that the sum is even.
The following table gives the probability distribution for X 5 number of wins in 3 plays of a game for which the chance of winning each game 5 .2, and plays are independent.X 5 Number of wins 0123 Probability .512 .384 .096 .008a. Find P(X # 1), the probability of winning one or fewer games in
The following table gives the probability distribution for X 5 number of classes skipped yesterday by students at a college.No. of Classes skipped, X 01234 Probability .73 .16 .06 .03 .02a. What is the probability that a randomly selected student skipped either two or three classes yesterday?b.
Suppose the probability distribution for X 5 number of jobs held during the past year for students at a school is as follows:No. of Jobs, X 01234 Probability .14 .37 .29 .15 .05a. Find P(X # 2), the probability that a randomly selected student held two or fewer jobs during the past year.b. Find the
For a fair coin tossed three times, the eight possible simple events are HHH, HHT, HTH, THH, HTT, THT, TTH, and TTT. Let X 5 number of heads. Find the probability distribution for X by writing a table showing each possible value of X along with the probability that the value occurs.
Answer Thought Question 8.3 on page 271.
For a large population, probabilities for X 5 the number of meals eaten yesterday are:Meals, X 1234 Probability .10 .32 .56 .02a. Write a table that gives the cumulative probability distribution for X.b. What is the value of P(X # 2), the probability that a randomly selected person ate two or fewer
A professor gives a weekly quiz with varying numbers of questions and uses a randomization device to decide how many questions to include. Let the random variable X 5 the number of questions on an upcoming quiz. The probability distribution for X is given in the following table, but one probability
What is the missing value, represented by the question mark(?) in each of the following probability distribution functions?a.k 1 4 57 P(X 5 k) 1/6 1/6 1/6 ?b.k 100 200 300 400 500 P(X 5 k) .1 .2 .3 .3 ?
Answer Thought Question 8.1 on page 266.
Explain the difference between how probabilities may be represented for discrete and continuous random variables.
Suppose you regularly play a lottery game. Give an example of a discrete random variable in this context
Refer to Example 8.1 (p. 264), the scheduling of an outdoor event. Give an example of another continuous random variable (in addition to temperature) and another discrete random variable (in addition to number of planes flying overhead) that would influence the enjoyment of the event. Give the
For each characteristic, explain whether the random variable is continuous or discrete.a. Time to read a news article on the Internet.b. Number of losing instant lottery tickets purchased before buying a winning ticket.c. Body weights of 8-year-old children.d. Number of people with brown eyes in a
For each characteristic, explain whether the random variable is continuous or discrete.a. The number of left-handed individuals in a sample of 100 people.b. Time taken to complete an exam for students in a class.c. Vehicle speeds at a highway location.d. The number of accidents reported last year
A book is randomly chosen from a library shelf. For each of the following characteristics of the book, decide whether the characteristic is a continuous or a discrete random variable:a. Weight of the book (e.g., 2.3 pounds).b. Number of chapters in the book (e.g., 10 chapters).c. Width of the book
Decide whether each of the following characteristics of a television news broadcast is a continuous or discrete random variable:a. Number of commercials shown (e.g., five commercials).b. Length of the first commercial shown (e.g., 15 seconds).c. Whether there were any fatal car accidents reported(0
Suppose that two people were randomly selected from that population. Given that one of them had been divorced, what is the probability that the other one had also been divorced?
Suppose that two people were randomly selected from that population, without replacement. What is the probability that they had both been divorced?
Suppose that two people were randomly selected from that population, without replacement. What is the probability that one of them smoked but the other one did not (in either order)?
Given that the person smoked, what is the probability that he or she had been divorced?
Given that the person had been divorced, what is the probability that he or she smoked?
What is the approximate probability that the person had ever been divorced?
What is the approximate probability that the person smoked?

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