Probability Test Review

Front

What is the expected value in probability?

Back

The expected value is the average outcome of a random variable, calculated as the sum of all possible values, each multiplied by its probability of occurrence.

Front

How do you calculate the expected value of a discrete random variable?

Back

Multiply each possible outcome by its probability and sum all these products.

Front

What is a normal distribution?

Back

A normal distribution is a continuous probability distribution characterized by a symmetric bell-shaped curve, defined by its mean and standard deviation.

Front

What does the mean represent in a probability distribution?

Back

The mean represents the average or central value of a set of data points in a probability distribution.

Front

What is the standard deviation in statistics?

Back

The standard deviation measures the amount of variation or dispersion in a set of values.

Front

What is the empirical rule in statistics?

Back

The empirical rule states that for a normal distribution, approximately 68% of data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.

Front

How do you find the probability of a range in a normal distribution?

Back

Use the Z-score formula to convert the range values to Z-scores, then refer to the standard normal distribution table to find the probabilities.

Front

What is a continuous random variable?

Back

A continuous random variable can take any value within a given range, as opposed to discrete variables which can only take specific values.

Front

What is the significance of the 68-95-99.7 rule?

Back

It provides a quick way to understand the spread of data in a normal distribution, indicating how much data falls within one, two, or three standard deviations from the mean.

Front

What is the formula for calculating the Z-score?

Back

Z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.