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elementary statistics

Questions and Answers of Elementary Statistics

A sample of 75 books is selected from a library. A: At least 10 of the authors are female; B: At least 10 of the books are fiction.In Exercises 25–30, determine whether events A and B are mutually
In a poll conducted by the General Social Survey, 497 out of 1769 people said that their main satisfaction in life comes from their work.a. What is the probability that a person who was polled finds
50C50 In Exercises 23–28, evaluate the combination.
A: The student is a freshman.B: The student is a sophomore.In Exercises 27–30, assume that a student is chosen at random from a class. Determine whether the events A and B are independent, mutually
A: The student is on the basketball team.B: The student is more than six feet tall.In Exercises 27–30, assume that a student is chosen at random from a class. Determine whether the events A and B
A red die and a blue die are rolled. A: The red die comes up 2; B: The blue die comes up 3.In Exercises 25–30, determine whether events A and B are mutually exclusive.
A local pizza parlor is offering a half-price deal on any pizza with one topping. There are eight toppings from which to choose. In addition, there are three different choices for the size of the
A red die and a blue die are rolled. A: The red die comes up 1; B: The total is 9.In Exercises 25–30, determine whether events A and B are mutually exclusive.
A: The student is a woman.B: The student belongs to a sorority.In Exercises 27–30, assume that a student is chosen at random from a class. Determine whether the events A and B are independent,
Josephine has six chemistry books, three history books, and eight statistics books. She wants to choose one book of each type to study. In how many ways can she choose the three books?
A: The student is a woman.B: The student belongs to a fraternity.In Exercises 27–30, assume that a student is chosen at random from a class. Determine whether the events A and B are independent,
A fair coin is tossed three times. The outcomes of the three tosses are recorded.a. List all eight outcomes in the sample space.b. Assuming the outcomes to be equally likely, find the probability
Let A and B be events with P (A) = 0.25, P (B) = 0.4, and P (A and B) = 0.1.a. Are A and B independent? Explain.b. Compute P (A or B).c. Are A and B mutually exclusive? Explain.
A sample of 225 Internet users was selected.a. More than 200 of them use Google as their primary search engine.b. At least 200 of them use Google as their primary search engine.c. Fewer than 200 of
A sample of 700 cell phone batteries was selected.a. Exactly 24 of the batteries were defective.b. At least 24 of the batteries were defective.c. More than 24 of the batteries were defective.d. Fewer
A coin is tossed 400 times and comes up heads 180 times. Use the Empirical Method to approximate the probability that the coin comes up heads.
A certain ice cream parlor offers 15 flavors of ice cream. You want an ice cream cone with three scoops of ice cream, all different flavors.a. In how many ways can you choose a cone if it matters
A die is rolled 600 times. On 85 of those rolls, the die comes up 6.Use the Empirical Method to approximate the probability that the die comes up 6.
During a recent season, pitcher Clayton Kershaw threw 2515 pitches. Of these, 1303 were fastballs, 12 were changeups, 385 were curveballs, and 815 were sliders.a. What is the probability that Clayton
Let A and B be events with P (A) = 0.4, P (B) = 0.5, and P (A or B) = 0.6.a. Compute P (A and B).b. Are A and B mutually exclusive? Explain.c. Are A and B independent? Explain.
Two fair dice are rolled. The first die is red and the second is blue. An experiment consists of observing the numbers that come up on the dice.a. There are 36 outcomes in the sample space. They are
Let A and B be events with P (A) = 0.6, P (B) = 0.9, and P (A and B) = 0.5.a. Are A and B independent? Explain.b. Compute P (A or B).c. Are A and B mutually exclusive? Explain.
A commuter passes through two traffic lights on the way to work. Each light is either red, yellow, or green. An experiment consists of observing the colors of the two lights.a. List the nine outcomes
In a certain state, license plates consist of four digits from 0 to 9 followed by three letters. Assume the numbers and letters are chosen at random. Replicates are allowed.a. How many different
The Student Council at a certain school has 10 members. Four members will form an executive committee consisting of a president, a vice president, a secretary, and a treasurer.a. In how many ways can
During a recent season, pitcher Jon Lester threw 3727 pitches. Of these, 1449 were thrown with no strikes on the batter, 1168 were thrown with one strike, and 1110 were thrown with two strikes.a.
Let A and B be events with P (A) = 0.5, P (B) = 0.3, and P (A or B) = 0.8.a. Compute P (A and B).b. Are A and B mutually exclusive? Explain.c. Are A and B independent? Explain.
Let E be the event that a new car requires engine work under warranty and let T be the event that the car requires transmission work under warranty. Suppose that P (E) = 0.10, P (T) = 0.02, and P (E
A company has hired 12 new employees, and must assign 8 to the day shift and 4 to the night shift.a. In how many ways can the assignment be made?b. Assume that the 12 employees consist of six men and
An automobile insurance company divides customers into three categories: good risks, medium risks, and poor risks. Assume that of a total of 11,217 customers, 7792 are good risks, 2478 are medium
A fair die is rolled three times. What is the probability that it comes up 6 at least once?
Let V be the event that a computer contains a virus, and let W be the event that a computer contains a worm. Suppose P (V) = 0.15, P (W) = 0.05, and P (V and W) = 0.03.a. Find the probability that
A computer password consists of eight characters. Replications are allowed.a. How many different passwords are possible if each character may be any lowercase letter or digit?b. How many different
A company audit showed that of 875 bills that were sent out, 623 were paid on time, 155 were paid up to 30 days late, 78 were paid between 31 and 90 days late, and 19 were paid after 90 days. One
An unfair coin has probability 0.4 of landing heads. The coin is tossed four times. What is the probability that it lands heads at least once?
Out of 800 large purchases made at a computer retailer, 336 were personal computers, 398 were laptop computers, and 66 were printers. As part of an audit, one purchase record is sampled at random.a.
Human genetic material (DNA) is made up of sequences of the molecules adenosine (A), guanine (G), cytosine (C), and thymine (T), which are called bases. A codon is a sequence of three bases.
A Nevada roulette wheel has 38 pockets. Eighteen of them are red, eighteen are black, and two are green. Each time the wheel is spun, a ball lands in one of the pockets, and each pocket is equally
Seven people, named Anna, Bob, Chandra, Darlene, Ed, Frank, and Gina, will be interviewed for a job.The interviewer will choose two at random to interview on the first day. What is the probability
A committee consists of 10 women and eight men. Three committee members will be chosen as officers.a. How many different choices are possible?b. How many different choices are possible if all the
A fast-food restaurant chain has 600 outlets in the United States. The following table categorizes them by city population size and location, and presents the number of restaurants in each category.
On a recent Saturday, a total of 1200 people visited a local library. Of these people, 248 were under age 10, 472 were aged 10–18, 175 were aged 19–30, and the rest were more than 30 years old.
Refer to Exercise 37.a. What is the probability that the ball lands in a green pocket?b. If you bet on green on every spin of the wheel, you will lose more than 90% of the time in the long run.
Charles has six songs on a playlist. Each song is by a different artist. The artists are Drake, Beyonce, Taylor Swift, The Weeknd, Calvin Harris, and Rihanna. He programs his player to play the songs
The General Social Survey asked 32,201 people how much confidence they had in educational institutions. The results were as follows.a. What is the probability that a sampled person has either some or
In a recent semester at a local university, 500 students enrolled in both Statistics I and Psychology I. Of these students, 82 got an A in statistics, 73 got an A in psychology, and 42 got an A in
In the game of Texas hold ’em, a player is dealt two cards (called hole cards) from a standard deck of 52 playing cards. The order in which the cards are dealt does not matter.a. How many different
The following table displays the 100 senators of the 115th U.S. Congress on January 3, 2017, viewed by political party affiliation and gender.A senator is selected at random from this group.a. What
The General Social Survey asked 46,349 women how many children they had. The results were as follows.a. What is the probability that a sampled woman has two children?b. What is the probability that a
There are 25 students in Mrs. Bush’s sixth-grade class. On a cold winter day in February, many of the students had runny noses and sore throats. After examining each student, the school nurse
According to the Agency for Healthcare Research and Quality, there were 409,706 hospital visits for asthma-related illnesses in a recent year. The age distribution was as follows.a. What is the
In a statistics class of 30 students, there were 13 men and 17 women. Two of the men and three of the women received an A in the course. A student is chosen at random from the class.a. Find the
In single-deck casino blackjack, the dealer is dealt two cards from a standard deck of 52.The first card is dealt face down and the second card is dealt face up.a. How many dealer hands are possible
On a certain day, a foundry manufactured 500 cast aluminum parts. Some of these had major flaws, some had minor flaws, and some had both major and minor flaws. The following table presents the
The Centers for Disease Control and Prevention reported that there were 443,000 smoking-related deaths in the United States in a recent year. The numbers of deaths caused by various illnesses
In the Georgia Fantasy 5 Lottery, balls are numbered from 1 to 42.Five balls are drawn. To win the jackpot, you must mark five numbers from 1 to 42 on a ticket, and your numbers must match the
In the Colorado Lottery Lotto game, balls are numbered from 1 to 42.Six balls are drawn. To win the jackpot, you must mark six numbers from 1 to 42 on a ticket, and your numbers must match the
A population of 600 semiconductor wafers contains wafers from three lots. The wafers are categorized by lot and by whether they conform to a thickness specification, with the results shown in the
The following table displays the 100 senators of the 115th U.S. Congress on January 3, 2017, classified by political party affiliation and gender.A senator is selected at random from this group.
Let A and B be events. Consider the following sentence:Each blank in the sentence can be filled in with either of two choices, as follows:(i) independent, mutually exclusive (ii) P (A and B), P (A or
If five fair coins are tossed, the possible outcomes for the number of heads obtained are 0, 1, 2, 3, 4, and 5.Use a computer simulation to toss five fair coins 1000 times and estimate the
The following table presents the number of reports of graffiti in each of New York’s five boroughs over a one-year period.These reports were classified as being open, closed, or pending.A graffiti
In a recent school year in the state of Washington, there were 326,000 high school students. Of these, 159,000 were girls and 167,000 were boys. Among the girls, 7800 dropped out of school, and among
In the game of Dungeons & Dragons, four-sided dice are rolled, with equally likely outcomes 1, 2, 3, and 4.If three four-sided dice are rolled, the possible totals are the numbers 3 through 12.Use a
The Bureau of Labor Statistics reported that 64.5 million women and 74.6 million men were employed. Of the women, 25.8 million had management jobs, and of the men, 25.0 million had management jobs.
In a certain high school, the probability that a student drops out is 0.05, and the probability that a dropout gets a high-school equivalency diploma (GED) is 0.25.What is the probability that a
Construct a sample space for this experiment that contains the 36 equally likely outcomes.Two dice are rolled. One is red and one is blue. Each will come up with a number between 1 and 6.There are 36
In a certain community, 28% of the houses have fireplaces and 51% have garages. Is the probability that a house has either a fireplace or a garage equal to 0.51 + 0.28 = 0.79? Explain why or why not.
What is the probability that the sum of the dice is 5?Two dice are rolled. One is red and one is blue. Each will come up with a number between 1 and 6.There are 36 equally likely outcomes for this
According to the National Health Statistics Reports, 16% of American women have one child, and 21%have two children. Is the probability that a woman has either one or two children equal to 0.16 +
The Bureau of Labor Statistics reported that the probability that a randomly chosen employed adult worked in a service occupation was 0.17, and given that a person was in a service occupation, the
Give an example of three events A, B, and C, such that A and B are mutually exclusive, B and C are mutually exclusive, but A and C are not mutually exclusive.
What is the probability that the sum of the dice is 7?Two dice are rolled. One is red and one is blue. Each will come up with a number between 1 and 6.There are 36 equally likely outcomes for this
At a certain car dealership, the probability that a customer purchases an SUV is 0.20. Given that a customer purchases an SUV, the probability that it is black is 0.25.What is the probability that a
Let A and B be events. Express (A and B)c in terms of Ac and Bc.
Now assume that you have rolled the red die, and it has come up 3.How many of the original 36 outcomes are now possible?Two dice are rolled. One is red and one is blue. Each will come up with a
According to a survey by Nickelodeon TV, 88% of children under 13 in Germany recognized a picture of the cartoon character SpongeBob SquarePants. Assume that among those children, 72% also recognized
Construct a sample space containing the outcomes that are still possible after the red die has come up 3.Two dice are rolled. One is red and one is blue. Each will come up with a number between 1 and
Given that the red die came up 3, what is the probability that the sum of the dice is 5? Is the probability the same as it was before the red die was observed?Two dice are rolled. One is red and one
Given that the red die came up 3, what is the probability that the sum of the dice is 7? Is the probability the same as it was before the red die was observed?Two dice are rolled. One is red and one
In a recent year, 21% of all vehicles in operation were pickup trucks. If someone owns two vehicles, is the probability that they are both pickup trucks equal to 0.21 × 0.21 = 0.0441? Explain why or
A traffic light at an intersection near Jamal’s house is red 50% of the time, green 40% of the time, and yellow 10% of the time. Jamal encounters this light in the morning on his way to work and
Every day, Jorge buys a lottery ticket. Each ticket has probability 0.2 of winning a prize. After seven days, what is the probability that Jorge has won at least one prize?
The probability that a certain make of car will need repairs in the first six months is 0.3. A dealer sells five such cars. What is the probability that at least one of them will require repairs in
In the game of tic-tac-toe, if all moves are performed randomly the probability that the game will end in a draw is 0.127. Suppose 10 random games of tic-tac-toe are played. What is the probability
Find the probability that the test gives the correct result for a person who does not have the disease.Exercises 59–62 refer to the following situation:A medical test is available to determine
The technology consulting company Data Genetics suggests that 17.8% of all four-digit personal identification numbers, or PIN codes, have a repeating digits format such as 2525. Assuming this to be
Given that a person gets a positive result, what is the probability that the person actually has the disease?Exercises 59–62 refer to the following situation:A medical test is available to
Find the probability that the test gives the correct result for a person who has the disease.Exercises 59–62 refer to the following situation:A medical test is available to determine whether a
For many medical tests, if the result comes back positive, the test is repeated. Why do you think this is done?Exercises 59–62 refer to the following situation:A medical test is available to
Let A and B be events.Assume that neither A nor B can occur; in other words, P (A) = 0 and P (B) = 0.Are A and B independent? Are A and B mutually exclusive? Explain.Exercises 59–62 refer to the
Let A and B be events. Now assume that P (A) = 0 but P (B) > 0.Are A and B always independent? Are A and B always mutually exclusive?Explain.Exercises 59–62 refer to the following situation:A
Let A and B be events. Now assume that P (A) > 0 and P (B) > 0.Is it possible for A and B to be both independent and mutually exclusive?Explain.Exercises 59–62 refer to the following situation:A
Explain why the following is not a probability distribution. x 6 7 8 9 10 P(x) 0.32 0.11 0.19 0.28 0.03
One of the most surprising probability distributions found in practice is given by a rule known as Benford’s law. This probability distribution concerns the first digits of numbers. The first digit
Provide an example of a discrete random variable and explain why it is discrete.
Determine whether X is a binomial random variable.a. A fair die is rolled 20 times. Let X be the number of times the die comes up 6.b. A standard deck of 52 cards contains four aces. Four cards are
A family has three children. If the genders of these children are listed in the order they are born, there are eight possible outcomes: BBB, BBG, BGB, BGG, GBB, GBG, GGB, and GGG. Assume these
The number of traffic accidents at a certain intersection follows a Poisson distribution with λ = 2 per year. Let X be the number of accidents that occur in a 4-year period.a. Find P(7).b. Find
Find the mean of the random variable X with the following probability distribution. x -2 1 4 5 P(x) 0.3 0.2 0.1 0.4

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