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Probability: a proportion representing the likelihood of an event ranging…
Probability: a proportion representing the likelihood of an event ranging from 0 to 1
Random Sampling: selecting individuals using chance rather than deliberately choosing them
Equal Chance of Selection:every individual in the population must have the same probability of being selected
Simple Random Sample: a sample in which each individual has an equal chance of being selected
Independent Random Sampling; each selection does not affect the probability of later selections
Independent Random Sample: a sample produced when the probability of selection remains constant from one selection to the next
Constant Probability: sampling with replacement keeps the probability of each possible outcome the same across selections
Sampling With Replacement: after someone/item is selected, it is returned to the population before the next selection
Sampling Without Replacement: selected individuals/items are not returned, so probabilities can change
Normal Distribution: probabilities for normally distributed scores can be determined using z-scores
z-Score: identifies a score's position relative to the mean in standard deviation units
formula for a sample: z = (x – μ) / σ
Unit Normal Table: uses z-scores to find proportions/probabilities in the standard normal distribution
X → z → Probability: Convert an X score to a z-score, then use the unit normal table to find its probability
Probability → z → X: start with a probability, find its corresponding z-score, then convert z back to an X value
Percentile: a statistical measure that shows the percentage of a dataset that falls at or below a specific value
Percentile Rank: the percentage of scores at or below a particular score
Area to the Left: the percentile rank corresponds to the proportion of the distribution at or below that score
Quartiles: divide a distribution into four equal sections each containing 25% of the scores
Interquartile Range (IQR): the distance between Q1 and Q3 representing the middle 50% of scores
Percentile: the X value associated with a particular percentile rank
Proportion: probability problems can be understood as proportion problems
Event: the specific outcome we want to know the probability of
Probability Formula P(A): outcomes classified as A ÷ total possible outcomes
Area Under a Distribution: an area represents a proportion, which can also represent a probability