Stats exam pt 6

A​ __________ random variable has either a finite or countable number of values.

discrete

The notation​ __________ is used for the number of trials in a binomial experiment.

n

As a rule of​ thumb, the probability distribution for a binomial random variable will be approximately​ bell-shaped if which condition is​ satisfied? p(1-p)≤10 np(1-p)≤10 p(1-p)≥10 np(1-p)≥10

np(1-p)≥10

The notation​ __________ is used for the probability of sucess on any trial in a binomial experiment.

p

Explain how to find the mean of a discrete random variable. A. To find the mean of a random​ variable, find the weighted average of the squared​ deviations, using the probabilities as weights. B. To find the mean of a random​ variable, multiply each value of the random variable by its probability and then add those products. C. To find the mean of a random​ variable, add the probabilities of each value and divide by the number of possible values. D. To find the mean of a random​ variable, add the possible values of the random variable and divide by the number of possible values

To find the mean of a random​ variable, multiply each value of the random variable by its probability and then add those products.

The notation​ __________ is used for the binomial random variable which counts the number of successes in n independent trials of an experiment.

x

four cards are selected from a standard​ 52-card deck without replacement. The number of queens selected is recorded. Does the probability experiment represent a binomial​ experiment? A. ​No, because the experiment is not performed a fixed number of times. B. ​No, because there are more than two mutually exclusive outcomes for each trial. C. ​No, because the trials of the experiment are not independent and the probability of success differs from trial to trial. Your answer is correct. D. ​Yes, because the experiment satisfies all the criteria for a binomial experiment.

​No, because the trials of the experiment are not independent and the probability of success differs from trial to trial.

The notation​ __________ is used for the probability of failure on any trial in a binomial experiment.

1-p

Describe how the value of n affects the shape of the binomial probability histogram. A. As n​ decreases, the binomial distribution becomes skewed left. B. As n​ increases, the binomial distribution becomes more bell shaped. Your answer is correct. C. As n​ increases, the binomial distribution becomes skewed right. D. As n​ decreases, the binomial distribution becomes more bell shaped. E. The value of n does not affect the shape of the binomial probability histogram

As n​ increases, the binomial distribution becomes more bell shaped.

The binomial probability distribution is a ​ __________ probability distribution that describes probabilities for experiments in which there are two​ __________ outcomes.

Discrete, mutually exclusive

Twenty percent of adults in a particular community have at least a​ bachelor's degree. Suppose x is a binomial random variable that counts the number of adults with at least a​ bachelor's degree in a random sample of 100 adults from the community. Which of the following probability statements indicates the probability that fewer than 30 adults have at least a​ bachelor's degree? P(x<30) P(x≥30) P(x≤30) P(x>30)

P(x<30)

Twenty percent of adults in a particular community have at least a​ bachelor's degree. Suppose x is a binomial random variable that counts the number of adults with at least a​ bachelor's degree in a random sample of 100 adults from the community. Which of the following probability statements indicates the probability that more than 30 adults have at least a​ bachelor's degree? P(x<30) P(x≥30) P(x≤30) P(x>30)

P(x>30)

Twenty percent of adults in a particular community have at least a​ bachelor's degree. Suppose x is a binomial random variable that counts the number of adults with at least a​ bachelor's degree in a random sample of 100 adults from the community. Which of the following probability statements indicates the probability that at most 30 adults have at least a​ bachelor's degree? P(x<30) P(x≥30) P(x≤30) P(x>30)

P(x≤30)

Twenty percent of adults in a particular community have at least a​ bachelor's degree. Suppose x is a binomial random variable that counts the number of adults with at least a​ bachelor's degree in a random sample of 100 adults from the community. Which of the following probability statements indicates the probability that at least 30 adults have at least a​ bachelor's degree? P(x<30) P(x≥30) P(x≤30) P(x>30)

P(x≥30)

​A(n) __________ is a numerical measure of the outcome of a probability experiment.

Random variable

For an experiment with a small number of​ trials, the binomial probability histogram will be​ __________ when the probability of success is greater than 0.5.

Skewed left

For an experiment with a small number of​ trials, the binomial probability histogram will be​ __________ when the probability of success is less than 0.5.

Skewed right

Suppose that a binomial random variable X is counting the number of patients with cancer at a particular hospital. How will​ "success" be defined in this​ situation? A. Success can be defined as selecting a patient who has cancer or as selecting a patient who does not have cancer. B. Success would be defined as selecting a patient at the hospital who has cancer. C. Success would be defined as selecting a patient at the hospital who does not have cancer. D. It is not possible to determine from this description how success should be defined.

Success would be defined as selecting a patient at the hospital who has cancer.

What is the mean of a probability​ distribution? A. The mean is the expected value of the random variable. B. The mean gives information on how the outcomes vary. C. The mean represents the most likely outcome for the random variable. D. The mean must be a possible value of the random variable.

The mean is the expected value of the random variable.

Identify which statement about the mean of a discrete random variable is not true or state that they are all true. A. The mean can be interpreted as the average outcome if the experiment is repeated many times. B. The mean must be a possible value of the random variable. C. The mean can be found using the formula D. All of these statements are true.

The mean must be a possible value of the random variable.

Identify the requirements for a discrete probability distribution. A. The sum of the probabilities must equal one. B. The sum of the probabilities must equal one. Each probability must be between zero and one inclusive. C. There must be a fixed number of independent trials. There must be two mutually exclusive outcomes for each trial with a constant probability of success. D. Each probability must be between zero and one inclusive.

The sum of the probabilities must equal one. Each probability must be between zero and one inclusive.

Which of the following is not a criterion for the binomial​ distribution? A. There must be a fixed number of trials. B. The trials must be dependent. C. There must be two disjoint outcomes for each trial. D. There must be a constant probability of success on each trial.

The trials must be dependent.

For an experiment with a small number of​ trials, the binomial probability histogram will be​ __________ when the probability of success is equal to 0.5.

approximately bell-shaped

According to an​ airline, flights on a certain route are on time 75% of the time. Suppose 13 flights are randomly selected and the number of​ on-time flights is recorded. Identify the statements that explain why this is a binomial experiment. Select all that apply. A. The probability of success is the same for each trial of the experiment. Your answer is correct. B. The trials are independent. Your answer is correct. C. The experiment is performed a fixed number of times. Your answer is correct. D. The experiment is performed until a desired number of successes is reached. E. Each trial depends on the previous trial. F. There are three mutually exclusive possibly​ outcomes, arriving​ on-time, arriving​ early, and arriving late. G. There are two mutually exclusive​ outcomes, success or failure.

A. The probability of success is the same for each trial of the experiment. B. The trials are independent. C. The experiment is performed a fixed number of times. G. There are two mutually exclusive​ outcomes, success or failure.

State the criteria for a binomial probability experiment. Choose the correct answer below. Select all that apply. A. The probability of​ success, p, remains constant for each trial of the experiment. B. Each trial has two possible mutually exclusive​ outcomes: success and failure. C. The experiment consists of a fixed​ number, n, of trials. D. The trials are independent.

A. The probability of​ success, p, remains constant for each trial of the experiment. B. Each trial has two possible mutually exclusive​ outcomes: success and failure. C. The experiment consists of a fixed​ number, n, of trials. D. The trials are independent.

An experimental drug is administered to 160 randomly selected​ individuals, with the number of individuals responding favorably recorded. Does the probability experiment represent a binomial​ experiment? A. ​Yes, because the experiment satisfies all the criteria for a binomial experiment. B. ​No, because the trials of the experiment are not independent. C. ​No, because there are more than two mutually exclusive outcomes for each trial. D. ​No, because the probability of success differs from trial to trial.

​Yes, because the experiment satisfies all the criteria for a binomial experiment.

An investor randomly purchases 16 stocks listed on a stock exchange.​ Historically, the probability that a stock listed on this exchange will increase in value over the course of a year is 46%. The number of stocks that increase in value is recorded. Does the probability experiment represent a biniomial​ experiment? A. ​Yes, because the experiment satisfies all the criteria for a binomial experiment. B. ​No, because the trials of the experiment are not independent. C. ​No, because there are more than two mutually exclusive outcomes for each trial. D. ​No, because the probability of success differs from trial to trial.

​Yes, because the experiment satisfies all the criteria for a binomial experiment.