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Probability:Probability is the chance or likelihood that something will…
Probability:Probability is the chance or likelihood that something will happen.
Probability helps inferential statistics determine how likely sample results are to represent the larger population. It helps us measure uncertainty and make predictions or conclusions from sample data.
Probability is written as p(outcome).
For example:
p(king) = probability of selecting a king
p(heads) = probability of getting heads on a coin toss
Probability is the likelihood that an event will happen. In inferential statistics, it helps us understand how likely our sample results are and make conclusions about a larger population.
Probability values are written as fractions or proportions that show how likely an event is to happen.
Random sampling means selecting outcomes by chance so that each outcome has an equal opportunity of being chosen.
A simple random sample gives every person in the population an equal chance of being selected.
Sampling with replacement means you return each person to the population after selecting them, so the probability stays the same for the next selection
Random sampling without replacement means selecting people randomly without putting them back, so the probability can change with each selection.
Percentile rank tells you the percentage of people who scored at or below a specific score.
percentile is the score that corresponds to a specific percentage of people at or below it.
Finding a percentile means using the unit normal table to find the z-score that matches a specific percentage of scores below it.
Q1 = 25th percentile
Q2 = 50th percentile (median)
Q3 = 75th percentile
IQR = Q3 − Q1
Independent random sampling means selecting people with replacement so each selection is independent and has the same probability.
Independent random sampling means the probability of selecting someone stays the same for each selection.
The normal distribution is a bell-shaped curve that shows how scores are distributed around the mean.
The equation determines the frequency (Y) for each score (X).
The unit normal table shows the proportion of scores for different z-scores. It helps you find the probability or percentage of scores in a normal distribution.
The unit normal table connects z-scores, proportions, and probabilities. You can use it to find a probability from a z-score or find a z-score from a probability.
For a normal distribution, the unit normal table gives the proportion or probability of scores at or below a specific z-score.
To find the probability between two scores, use the unit normal table and subtract the smaller proportion from the larger one. Column D can make this easier.
Use the unit normal table to find the probability or proportion associated with a given z-score.
Probability is the fraction of possible outcomes that result in event A.
p(A) = favorable outcomes ÷ total possible outcomes.
The role of probability in inferential statistics