Unit 6 - Probability Distributions

Front

What is a probability distribution?

Back

A probability distribution is a mathematical function that describes the likelihood of obtaining the possible values that a random variable can take.

Front

Define mean in the context of probability distributions.

Back

The mean is the average value of a set of numbers, calculated by summing all values and dividing by the number of values.

Front

What is standard deviation?

Back

Standard deviation is a measure of the amount of variation or dispersion in a set of values.

Front

Explain the Empirical Rule.

Back

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

Front

What is a binomial distribution?

Back

A binomial distribution is a discrete probability distribution that describes the number of successes in a fixed number of independent Bernoulli trials, each with the same probability of success.

Front

What are the assumptions of a binomial distribution?

Back

1. Fixed number of trials. 2. Each trial is independent. 3. Each trial has two possible outcomes (success or failure). 4. The probability of success is constant.

Front

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

Back

The expected value is calculated by multiplying each possible outcome by its probability and summing all these products.

Front

What does P(X ≤ k) represent in probability?

Back

P(X ≤ k) represents the probability that the random variable X takes on a value less than or equal to k.

Front

What is the significance of the normal distribution in statistics?

Back

The normal distribution is significant because many statistical methods assume normality, and it describes how data is distributed in many natural phenomena.

Front

How do you interpret a z-score?

Back

A z-score indicates how many standard deviations an element is from the mean. A positive z-score means the value is above the mean, while a negative z-score means it is below.