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elementary statistics
Questions and Answers of
Elementary Statistics
In a recent Pew poll, 50% of adults said that they play video games. Assume that 9 adults are randomly sampled.a. Use the binomial probability distribution to compute the probability that exactly
Provide an example of a continuous random variable and explain why it is continuous.
In a recent Pew poll, 10% of adults said that they consider themselves to be “gamers.”Assume that 18 adults are randomly sampled.a. Use the binomial probability distribution to compute the
Refer to Problem 2.a. Find the variance of the random variable X.b. Find the standard deviation of the random variable X.Problem 2Find the mean of the random variable X with the following probability
Someone says that the following table shows the probability distribution for the number of boys in a family of four children. Is this possible? Explain why or why not. x 0 1 2 3 4 P(x) 0.12 0.37 0.45
The number of hits on a certain website follows a Poisson distribution with λ = 12 per minute. Let X be the number of hits that occur in a period of one-half minute.a. Find P(5).b. Find P(Less than
Which of the following tables represent probability distributions? a. x P(x) b. x P(x) C. x P(x) 0 0.45 4 0.27 1 0.02 1 0.15 5 0.15 2 0.41 2 0.30 6 0.11 3 0.24 3 0.10 7 0.34 4 0.33 8 0.25
When a population mean is unknown, people will often approximate it with the mean of a large sample. Explain why this is justified.
An environmental scientist is counting the number of bacteria in a sample of wastewater. The number of bacteria has a Poisson distribution with λ = 3 per microliter. What is the probability that
Find the missing value that makes the following a valid probability distribution. x 2 3 5 8 10 P(x) 0.23 0.12 0.09 ? 0.37
Gregor Mendel discovered the basic laws of heredity by studying pea plants. In one experiment, he produced plants whose parent plants contained genes for both green and yellow pods. Mendel’s theory
During a recent academic year, approximately 1.7 million students took one or more AP tests. Following is the frequency distribution of the number of AP tests taken by students who took one or more
Following is the probability distribution of a random variable that represents the number of extracurricular activities a college freshman participates in.a. Find the probability that a student
In the Georgia Cash 3 Lottery game, your probability of winning is 0.001. The game is played twice daily, so 730 games are played in a year. If you play twice a day for a year, what is the
The following table presents a probability distribution for the number of pets each family has in a certain neighborhood.Construct a probability histogram. Number of pets Probability 012 3. 4 0.4 0.2
Provide an example of a binomial random variable and explain how each condition for the binomial distribution is fulfilled.
In a binomial distribution, there are _______________ possible outcomes for each trial.In Exercises 5–7, fill in each blank with the appropriate word or phrase.
There are 5000 undergraduates registered at a certain college. Of them, 478 are taking one course, 645 are taking two courses, 568 are taking three courses, 1864 are taking four courses, 1357 are
The Poisson distribution is used to describe events that occur in ______________ or _____________ .In Exercises 5 and 6, fill in each blank with the appropriate word or phrase.
Refer to Problem 5.Find the probability that a randomly selected family has:a. 1 or 2 petsb. More than 2 petsc. No more than 3 petsd. At least 1 petProblem 5The following table presents a probability
Following is a probability histogram for the number of children a woman has. The numbers on the tops of the rectangles are the heights.a. What is the probability that a randomly chosen woman has
To compute a binomial probability, we must know both the success probability and the number n of ___________________ .In Exercises 5–7, fill in each blank with the appropriate word or phrase.
Refer to Problem 5.Find the mean number of pets.Problem 5The following table presents a probability distribution for the number of pets each family has in a certain neighborhood.Construct a
The mean of the Poisson random variable X with rate λ and interval length t is __________________ .In Exercises 5 and 6, fill in each blank with the appropriate word or phrase.
Provide an example of a Poisson random variable and explain how each condition for the Poisson distribution is fulfilled.
If X is a binomial random variable with n trials and success probability p, the standard deviation of X isσX = __________________ .In Exercises 5–7, fill in each blank with the appropriate word or
Refer to Problem 5.Find the standard deviation of the number of pets.Problem 5The following table presents a probability distribution for the number of pets each family has in a certain
A true–false quiz with 10 questions was given to a statistics class. Following is the probability distribution for the score of a randomly chosen student. Find the mean score and interpret the
For a Poisson random variable with rate λ and time interval t, the possible values of x are 0, 1, 2, ..., λ.
Following is the probability distribution for the age of a student at a certain public high school.a. Find the variance of the ages.b. Find the standard deviation of the ages. x 13 14 15 16 17 18
The trials in a binomial distribution are independent.In Exercises 8–10, determine whether the statement is true or false. If the statement is false, rewrite it as a true statement.
A binomial random variable with n trials can sometimes have a value greater than n.In Exercises 8–10, determine whether the statement is true or false. If the statement is false, rewrite it as a
In a Poisson distribution, the mean and variance are equal.
At a cell phone battery plant, 5% of cell phone batteries produced are defective. A quality control engineer randomly collects a sample of 50 batteries from a large shipment from this plant and
A numerical outcome of a probability experiment is called a ____________.In Exercises 9–12, fill in each blank with the appropriate word or phrase.
λ = 2, t = 5, P(5)In Exercises 9–18, determine the indicated probability for a Poisson random variable with the given values of λ and t.
Refer to Problem 9.Find the mean and standard deviation for the number of defective batteries in the sample of size 50.Problem 9At a cell phone battery plant, 5% of cell phone batteries produced are
Let X be the number of days during the next month that it rains. Does X have a binomial distribution?Why or why not?
The mean of a binomial random variable is found by multiplying the number of trials by the success probability.In Exercises 8–10, determine whether the statement is true or false. If the statement
The sum of all the probabilities in a discrete probability distribution must be equal to _____________ .In Exercises 9–12, fill in each blank with the appropriate word or phrase.
λ = 0.5, t = 4, P(3)In Exercises 9–18, determine the indicated probability for a Poisson random variable with the given values of λ and t.
A meteorologist states that the probability of rain tomorrow is 0.4 and the probability of rain on the next day is 0.6.Assuming these probabilities are accurate, and that the rain events are
In a college with 5000 students, 100 are randomly chosen to complete a survey in which they rate the quality of the cafeteria food. Let X be the number of freshmen who are chosen. Does X have a
Ten students are chosen from a statistics class of 25 students.Let X be the number who got an A in the class.In Exercises 11–16, determine whether the random variable X has a binomial distribution.
λ = 0.1, t = 10, P(2)In Exercises 9–18, determine the indicated probability for a Poisson random variable with the given values of λ and t.
The number of large packages delivered by a courier service follows a Poisson distribution with a rate of 5 per day. Find the probability thata. Exactly 4 large packages are delivered on a given
Ten students are chosen from a statistics class of 300 students.Let X be the number who got an A in the class.In Exercises 11–16, determine whether the random variable X has a binomial
As the sample size increases, the sample mean approaches the _______________ mean.In Exercises 9–12, fill in each blank with the appropriate word or phrase.
λ = 1, t = 2, P(0)In Exercises 9–18, determine the indicated probability for a Poisson random variable with the given values of λ and t.
The number of text messages received on a certain person’s cell phone follows a Poisson distribution with the rate of 10 messages per hour. What is the mean number of messages received in an 8-hour
Refer to Exercise 12.Find the mean number of particles that are withdrawn.Exercise 12The concentration of particles in a suspension is 2 per milliliter. A volume of 3 milliliters is withdrawn.Find
A coin is tossed seven times. Let X be the number of heads obtained.In Exercises 11–16, determine whether the random variable X has a binomial distribution. If it does, state the number of trials
To find the mean of a discrete random variable, multiply each possible value of the random variable by its probability, then add the products.In Exercises 13–16, determine whether the statement is
λ = 0.2, t = 10, P(At least one)In Exercises 9–18, determine the indicated probability for a Poisson random variable with the given values of λ and t.
Refer to Problem 13.What are the variance and standard deviation of the number of messages received in an 8-hour period?Problem 13The number of text messages received on a certain person’s cell
Refer to Exercise 12.Find the standard deviation of the number of particles that are withdrawn.Exercise 12The concentration of particles in a suspension is 2 per milliliter. A volume of 3 milliliters
A die is tossed three times. Let X be the sum of the three numbers obtained.In Exercises 11–16, determine whether the random variable X has a binomial distribution. If it does, state the number of
The expected value is the mean amount gained or lost.In Exercises 13–16, determine whether the statement is true or false. If the statement is false, rewrite it as a true statement.
λ = 0.3, t = 8, P(At least one)In Exercises 9–18, determine the indicated probability for a Poisson random variable with the given values of λ and t.
Huntington’s disease is a genetically transmitted disease that causes degeneration of nerve cells in the brain. The probability that a person carries a gene for Huntington’s disease is 0.00005
A coin is tossed until a head appears. Let X be the number of tosses.In Exercises 11–16, determine whether the random variable X has a binomial distribution. If it does, state the number of trials
The possible values of a discrete random variable cannot be listed.In Exercises 13–16, determine whether the statement is true or false. If the statement is false, rewrite it as a true statement.
λ = 1, t = 4, P(No more than 5)In Exercises 9–18, determine the indicated probability for a Poisson random variable with the given values of λ and t.
A random sample of 250 voters is chosen from a list of 10,000 registered voters. Let X be the number who support the incumbent mayor for reelection.In Exercises 11–16, determine whether the random
The standard deviation is found by squaring the variance.In Exercises 13–16, determine whether the statement is true or false. If the statement is false, rewrite it as a true statement.
λ = 0.2, t = 7, P(More than 2)In Exercises 9–18, determine the indicated probability for a Poisson random variable with the given values of λ and t.
n = 5, p = 0.7, P(3)In Exercises 17–26, determine the indicated probability for a binomial experiment with the given number of trials n and the given success probability p. Then find the mean,
The number of heads in 100 tosses of a coin In Exercises 17–26, determine whether the random variable described is discrete or continuous.
n = 10, p = 0.2, P(1)In Exercises 17–26, determine the indicated probability for a binomial experiment with the given number of trials n and the given success probability p. Then find the mean,
The number of people in line at the bank at a randomly chosen time In Exercises 17–26, determine whether the random variable described is discrete or continuous.
λ = 0.3, t = 5, P(Fewer than 3)In Exercises 9–18, determine the indicated probability for a Poisson random variable with the given values of λ and t.
n = 20, p = 0.6, P(8)In Exercises 17–26, determine the indicated probability for a binomial experiment with the given number of trials n and the given success probability p. Then find the mean,
The weight of a randomly chosen student’s backpack In Exercises 17–26, determine whether the random variable described is discrete or continuous.
In a certain city, the number of potholes on a major street has a Poisson distribution with a rate of 3 per mile. Let X represent the number of potholes in a 2-mile stretch of road.Finda. P(4)b.
n = 14, p = 0.3, P(8)In Exercises 17–26, determine the indicated probability for a binomial experiment with the given number of trials n and the given success probability p. Then find the mean,
The amount of rain during the next thunderstorm In Exercises 17–26, determine whether the random variable described is discrete or continuous.
The number of flaws in a given area of aluminum foil follows a Poisson distribution with a mean of 3 per square meter. Let X represent the number of flaws in a 1-square-meter sample of foil.a. P(5)b.
n = 3, p = 0.4, P(0)In Exercises 17–26, determine the indicated probability for a binomial experiment with the given number of trials n and the given success probability p. Then find the mean,
The number of children absent from school on a randomly chosen day In Exercises 17–26, determine whether the random variable described is discrete or continuous.
The number of flaws in a certain type of lumber has a Poisson distribution with a rate of 0.5 per meter of length.a. What is the probability that a board 3 meters in length has no flaws?b. What is
n = 6, p = 0.8, P(6)In Exercises 17–26, determine the indicated probability for a binomial experiment with the given number of trials n and the given success probability p. Then find the mean,
The time it takes to drive to the airport In Exercises 17–26, determine whether the random variable described is discrete or continuous.
The number of times that screen flicker appears in video recorded on a certain type of digital video recorder (DVR) has a Poisson distribution with a rate of 0.2 per minute.a. What is the probability
n = 8, p = 0.2, P(Fewer than 3)In Exercises 17–26, determine the indicated probability for a binomial experiment with the given number of trials n and the given success probability p. Then find the
The final exam score of a randomly chosen student from last semester’s statistics class In Exercises 17–26, determine whether the random variable described is discrete or continuous.
The number of tweets received by a certain Twitter user is a Poisson random variable with a mean rate of 8 tweets per hour.a. What is the probability that 5 tweets are received in a given hour?b.
n = 15, p = 0.9, P(14 or more)In Exercises 17–26, determine the indicated probability for a binomial experiment with the given number of trials n and the given success probability p. Then find the
The amount of time you wait at a bus stop In Exercises 17–26, determine whether the random variable described is discrete or continuous.
Grandma bakes chocolate chip cookies in batches of 100.She puts 600 chips into each batch, so that the number of chips in a randomly chosen cookie has a Poisson distribution with λ = 6 chips per
n = 50, p = 0.03, P(2 or fewer)In Exercises 17–26, determine the indicated probability for a binomial experiment with the given number of trials n and the given success probability p. Then find the
The height of a randomly chosen college student In Exercises 17–26, determine whether the random variable described is discrete or continuous.
The number of trees of a certain species in a certain forest has a Poisson distribution with mean of 10 trees per acre.a. What is the probability that there will be exactly 18 trees in a 2-acre
n = 30, p = 0.9, P(More than 27)In Exercises 17–26, determine the indicated probability for a binomial experiment with the given number of trials n and the given success probability p. Then find
The number of songs on a randomly chosen iPod In Exercises 17–26, determine whether the random variable described is discrete or continuous.
In Exercises 27–32, determine whether the table represents a discrete probability distribution. If not, explain why not. x P(x) 1 0.4 23 0.2 3 0.1 4 0.3
An environmental scientist obtains a sample of water from a pond that contains a certain type of bacteria at a concentration of 5 per milliliter.a. What is the probability that there will be exactly
Match each TI-84 PLUS calculator command with the probability being calculated.a. 1 - binomcdf (n, p, 5)b. binompdf (n, p, 0)c. binompdf (n, p, 5)d. binomcdf (n, p, 5) - binompdf (n, p, 0)i.
In a recent year, there were approximately 250,000,000 registered motor vehicles in the United States. Of these, approximately 4% were involved in an accident during the year. Assume that a simple
In Exercises 27–32, determine whether the table represents a discrete probability distribution. If not, explain why not. P(x) 30 0.2 40 0.2 50 0.2 60 0.2 70 0.2
Match each TI-84 PLUS calculator command with the probability being calculated.a. binomcdf (n, p, 5)b. 1 - binompdf (n, p, 0)c. binomcdf (n, p, 5) - binomcdf (n, p, 2)d. binompdf (n, p, 1) + binompdf
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