Section A: Probability

What are mutually exclusive events?

If the occurrence of one event means that another event or events cannot occur, the events are said to be mutually exclusive. Only one of the events can possibly occur.

What are the properties of normal distributions?

* The inflection points are at exactly −1σ and +1σ. Inflection points are where the curve changes from bending upward to bending over. * The mean, median, and mode are the same, at the point on the x-axis where the curve peaks. * The mean divides the population in half. * The curve never ends; i.e., the tails of the curve never cross the x-axis. * The probabilities of a value falling within a given interval are marked by numbers of standard deviations from the mean.

What are the three methods used to assign probable values to possible outcomes?

1 Classical Method: This method assumes that each possible outcome has an equal probability of occurring. Thus, if there are ten possible outcomes, each outcome is assumed to have a 10% probability of occurring. 2 Relative Frequency or Objective Method: When factual information is available that can be used to determine the probability of something occurring, the use of that information to assign probabilities is called the relative frequency method. The information may come from a sample, analytical data, or any other reliable source. 3 Subjective Method: This method is used when neither the classical nor the relative frequency methods can be used. With the subjective method of assigning probabilities, we use whatever data is available and add to that data our own experience and intuition. After considering all available information, we assign a probable value that expresses our degree of belief that the outcome will occur.

In a normal distribution, what percent of values lie within one, two, and three standard deviations of the mean?

68.26% of the values lie within one standard deviation of the mean. 95.44% of the values lie within two standard deviations of the mean. 99.74% of the values lie within three standard deviations of the mean.

What is a continuous random variable?

A continuous random variable is a random variable that can take on any value within an interval (could be a fraction or decimal).

What is a discrete random variable?

A discrete random variable is a random variable that always has whole number values (no fractions or decimals).

What is a probability distribution?

A probability distribution is a table or an equation that links each outcome of a statistical experiment with its probability of occurring.

What is a random variable?

A random variable is a variable that can have any value within a range of values that occurs randomly and can be described using probabilities.

What is joint probability?

Joint probability is the probability of two or more events occurring at the same time. The joint probability of two independent events occurring at the same time is the independent probability of the first event multiplied by the independent probability of the second event.

What are the measures of central tendency?

Mean, median, and mode are measures of central tendency.

What is probability?

Probability gives us a numerical measurement of the likelihood that an event will occur.

How is probability expressed?

Probability is always expressed as a value between 0 and 1, and this expression is usually converted to a percentage between 0 and 100.

What is conditional probability?

The conditional probability of two events is the probability that the second event will occur when it is known that the first event has already occurred. Conditional probability deals with events that are not independent.

What is the expected value of a discrete random variable?

The expected value of a discrete random variable is the weighted average of all the possible values of the random variable. The weights are the probabilities for each of the values.

What is the mean of a set of numbers?

The mean is the average of a set of numbers.

What is the median of a set of numbers?

The median is the halfway value if raw data is arranged in numerical order from lowest to highest.

What is the mode of a set of numbers?

The mode is the most frequently occurring value in a set of numbers. If all values are unique (different from each other), no mode exists.

What is the normal probability distribution?

The normal probability distribution is the most important distribution, and it is often found in both nature and in human-made things. When graphed, it has the form of a bell-shaped curve centered on its mean.

What are the two requirements of probability?

The probability values assigned to each of the possible outcomes must be between 0 and 1. The probable values assigned to all of the possible outcomes must total 1.

What is the standard deviation of a probability distribution?

The standard deviation of a set of data is a measure of the degree of dispersion of the data from the mean value. The standard deviation is the positive square root of the variance. It is represented by σ (sigma).

What is the variance of a probability distribution?

Variance is used to summarize the variability in the values of a random variable. The variance is the sum of the squares of all the differences or deviations from the mean (average), weighted according to their probabilities. It is represented by σ2 (sigma squared).