Chapter 6

On average, 12 customers use the bank's ATM during the noon lunch hour. What is the probability that exactly 10 customers will use the ATM during the next noon lunch hour? Assume the Poisson distribution applies.

0.105

The table provides binomial probabilities for n=10. If 30% of adults take a vacation each year, what is the probability that four of 10 randomly sampled adults would indicate they take a vacation every year?

0.200

A bowl contains two red and three black marbles. A marble is randomly selected, its color noted, and returned to the bowl. Let "success" be selecting a red marble. Use the binomial probability formula to find the chance of selecting three red marbles in eight draws.

0.279

A bake shop sells twenty different kinds of pastries. Twelve of them were chocolate. Zack randomly buys eight kinds of pastries. What is the chance that four of them will be chocolate? Use the hypergeometric distribution.

0.28

Which of the following statements describe the Poisson Distribution? Select all that apply

The random variable is the number of occurrences during an interval. The intervals do not overlap and are independent. The probability of the event is proportional to the interval size.

Which of the following formulas is the easiest way to calculate the mean of a binomial distribution?

μ = nπ

Which of the following formulas is the easiest way to calculate the variance of a binomial distribution?

σ2 = nπ(1 - π)

A restaurant employs 16 people, 8 of whom are women. If five employees are chosen randomly to receive tickets to a concert, what is the probability (to two decimal places) that three of them will be women? Use the hypergeometric distribution.

0.36

A grocer checks 200 apples and finds that 8 are spoiled. On average, how many apples are spoiled in a bag of ten? (Hint: spoilage will follow a Poisson distribution, let n=10 and π is the empirical probability.)

0.40

Calculate the mean for the probability distribution shown here.

3.4 Reason: μ = Σ[xP(X)]=(0*.1)+(2*.3)+(4*.4)+(6*.2)

A binomial distribution has n = 12 trials with a probability of success of π=0.3. Calculate the mean of this binomial distribution.

3.60

A binomial distribution has n = 10 trials with a probability of success of π=0.4. Calculate the mean of this binomial distribution,.

4.0

What shows the possible outcomes of a random experiment and the probability of each outcome?

A Probability Distribution

Which of the following statements best describes a Probability Distribution?

A list of the outcomes of a random experiment and the probability of each outcome.

What is a Discrete Random Variable?

A random variable that can assume only separate distinct values.

Which of the following statements is true for both the binomial and Poisson distributions?

Both are discrete probability distributions.

Which of the following statements describes the relationship between the Poisson distribution and the binomial distribution?

It is a limiting form of the binomial distribution when the probability of success (π) is very small and the sample (n) is very large.

Choose the statements that describe characteristics of a Probability Distribution. Select all that apply.

The sum of the probabilities of all possible outcome is one. The probability of an outcome is between 0 and 1 inclusive. The outcomes are mutually exclusive events.

In a binomial experiment the variable is the number of successes in a fixed number of trials and the probability of success is the same for each trial. Which two of the following statements also describe features of a binomial experiment?

Trials are independent. The outcome of a trial can be classified as either a success or a failure.

True or false: The standard deviation of a probability distribution is the square root of the variance of the probability distribution.

True

It is easier to use a binomial probability table instead of calculating the probability under what circumstances?

When n is large.

Under what circumstances should you use the hypergeometric distribution instead of the binomial distribution?

When the probability of success changes for each trial.

When can a binomial distribution be used as a good approximation to a hypergeometric distribution?

When the sample size (n) is less than 5% of the population.

A random variable can be defined as:

a quantity resulting from a random experiment that can have different values

The formula for the mean of a binomial distribution is μ = nπ. What do the symbols n and π represent in this formula?

number of trials and P(success)

Suppose that 25% of adults exercise regularly. If 11 adults randomly selected, what is the probability that four or less exercise regularly? Assume the binomial distribution applies.

0.885

Suppose that 40% of households use their cell phones for their home phone. If 12 households are randomly selected, what is the probability that at least three use their cell phones? Assume the binomial distribution applies.`

0.917

A binomial distribution has 8 trials and a probability of success of 0.2. Calculate the variance for this distribution.

1.28

A binomial distribution has 12 trials and a probability of success of 0.4. Calculate the variance for this distribution.

2.88

Choose the random variables from this set that are discrete. Select all that apply.

Number of drive-thru customers to the bank on a given day. The number of dots uppermost of rolling a pair of dice.

Suppose a problem asks for the probability of at most four successes when there are only five trials. Which one of these expressions would provide the answer?

P(x=0) + P(x=1) + P(x=2) + P(x=3) + P(x=4)

A quantity representing the outcome of a random experiment that can assume different values is called a:

Random Variables

From the following list, choose the random variables that are continuous. Select all that apply.;

The average annual return on a certain bond. The tire pressure in a randomly selected automobile.

Choose the two random variables from this list that are continuous.

The average temperature in NYC during May. The wait time at the dentist.

Which of the following statements are not true of the Poisson Distribution?

The intervals overlap and are not independent.

A Binomial experiment has independent trials and the outcome of a trial can be classified as either a success or a failure. Which two of the following statements also describe features of a binomial experiment?

The random variable counts the number of successes in a fixed number of trials. The probability of success stays the same for each trial.