QMET 251 - Exam 2

If two events are mutually exclusive, what is the probability that both occur at the same time?

0

The smallest number of possible successes in a Poisson distribution is:

0

The smallest number of possible successes in a binomial distribution is

0

The smallest possible value for a probability is ______.

0

The largest possible value for a probability is ______.

1

The sum of the probabilities of all the events in a probability distribution is equal to:

1

List the properties of the Normal Distribution:

1. the equation for the graph of the distribution is given by : 2. The distribution is completely defined by two parameters: its mean and standard deviation 3. distribution is bell-shaped and symmetric about its mean u. 4. The standard deviation is the distance from a vertical line at u to where the curvature of the graph changes on either side. 5. The distribution is continuous, extending from -infinity to +infinity. 6. the x-axis is a horizontal asymptote for the curve (the graph never touches the x-axis) 7. the total area bounded by the curve and the horizontal axis is 1, with 0.5 area to the left of u and 0.5 area to the right of u. 8. the mean, median, and mode coincide.

If two events are collectively exhaustive, what is the probability that one or the other occurs?

1.00

In estimating the population mean with the population standard deviation unknown, if the sample size is 12, there will be _____ degrees of freedom.

11

A computer lab at a university has ten personal computers. Based on past experience, the probability that any one of them will require repair on a given day is 0.05. To find the probability that exactly two of the computers will require repair on a given day, you can use what probability distribution?

Binomial distribution

A multiple-choice test has 25 questions. There are four choices for each question. A student who has not studied for the test decides to answer all questions by randomly choosing one of the four choices. What probability distribution can be used to compute his chance of correctly answering at least 15 questions?

Binomial distribution

The ________ is important in statistics because it states that the sampling distribution of the sample mean is approximately normally distributed for a large sample size n regardless of the shape of the population.

Central Limit Theorem

The sampling distribution of the mean can be approximated by the normal distribution when the sample size of all possible samples gets large enough.

Central Limit Theorem

T/F: A sampling distribution is defined as the probability distribution of possible sample sizes that can be observed from a given population.

False

T/F: In the construction of confidence intervals, if all other quantities are unchanged, an increase in the sample size will lead to a wider interval.

False

T/F: the confidence interval estimate that is constructed will always correctly estimate the population parameter.

False

Based on past experience, the time you spend on emails per day has a mean of 30 minutes and a standard deviation of 10 minutes. To compute the probability of spending at least 12 minutes on emails, you can use what probability distribution?

Normal Distribution

The mean number of customers who arrive per minute at any one of the checkout counters of a grocery store is 1.8. What probability distribution can be used to find out the probability that there will be no customers arriving at a checkout counter in the next minute?

Poisson distribution

The probability distribution of a sample statistic for all possible samples of a give size n for a given population.

Sampling Distribution

T/F: The t distribution is used to construct confidence intervals for the population mean when the population standard deviation is unknown.

True

The sampling distribution of the mean requires ______ sample size to reach a normal distribution if the population is skewed than if the population is symmetrical.

a larger

Whenever p = 0.5, the binomial distribution will:

always be symmetric

The sampling distribution of the mean can be approximated by the normal distribution:

as the sample size (number of observations in each sample) gets large enough

If two events are collectively exhaustive, what is the probability that both occur at the same time? a. 0 b. 0.50 c. 1.00 d. cannot be determined from the information given

d. cannot be determined by the information given

Which of the following about the binomial distribution is not a true statement? a. the probability of success must be constant from trial to trial. b. each outcome is independent of the other. c. each outcome may be classified as either "success" or "failure" d. the variable of interest is continuous

d. the variable of interest is continuous

In the ______ probability approach, probabilities are based on frequencies obtained from surveys.

empirical

T/F: The diameters of 100 randomly selected bolts follow a binomial distribution.

false

For samples of n = 1, the sampling distribution of the mean will be normally distributed:

if the population is normally distributed

If the outcome of event A is not affected by event B, then events A and B are said to be:

independent

If two events are _______, the probability that both events occur is the product of their individual probabilities.

independent

If two events are ________, they cannot occur at the same time.

mutually exclusive

The largest number of possible successes in a binomial distribution is:

n

in the construction of confidence intervals, if all other quantities are unchanged, an increase in the sample size will lead to a ________ interval.

narrower

For samples of n = 30, for most populations, the sampling distribution of the mean will be approximately normally distributed:

regardless of the shape of the population

Sampling distributions describe the distribution of:

statistics

In the _______ probability approach, probabilities can vary depending on the individual assigning them.

subjective

The normal distribution is ______ in shape.

symmetric

For samples of n = 15, the sampling distribution of the mean will be normally distributed if the shape of the population is _______.

symmetrical

The probability that Z is less than -1.0 is ______ the probability that Z is greater than +1.0.

the same as

T/F: Another name for the mean of a probability distribution is its expected value.

true

T/F: As the sample size increases, the effect of an extreme value on the sample mean becomes smaller.

true

T/F: Other things being equal, as the confidence level for a confidence interval increases, the width of the interval increases.

true

T/F: Theoretically, the mean, median, and the mode are all equal for a normal distribution.

true

T/F: if the data values are normally distributed, the normal probability plot will follow a straight line.

true