What is a probability distribution?
A model describing how probabilities are distributed across possible outcomes of a variable.
What is a discrete variable?
A variable that can only take specific, separate values (e.g., number of tests passed).
What is a continuous variable?
A variable that can take any value within a range (e.g., height, time).
What is the normal distribution?
A bell-shaped, symmetric distribution that describes many natural phenomena. The mean = median = mode.
What is the standard normal distribution?
A normal distribution with mean = 0 and standard deviation = 1. Used for z-scores.
What is a z-score?
A standardized value that measures how many standard deviations an observation is from the mean. z = (x - μ)/σ.
What does a z-score of 0 mean?
The observation is exactly at the mean of the distribution.
What does a positive z-score indicate?
The value is above the mean.
What does a negative z-score indicate?
The value is below the mean.
What is the area under the normal curve equal to?
The total probability = 1 (or 100%).
What is the empirical rule for normal distributions?
Approximately 68% of data lie within 1 SD, 95% within 2 SD, and 99.7% within 3 SD of the mean.
What is a sampling distribution?
The probability distribution of a statistic (like the sample mean) over many samples from the same population.
What happens to the sampling distribution as sample size increases?
It becomes narrower and approximates the population mean more accurately (Central Limit Theorem).
What is the Central Limit Theorem?
As sample size increases, the sampling distribution of the sample mean approaches a normal distribution, regardless of population shape.
