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PROBABILITY - Coggle Diagram
PROBABILITY
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Random sampling requires that each individual in the population has an equal chance of being selected. A sample obtained by this process is called a simple random sample.
an independent random sample is usually a required component for most statistical applications,
The term independent refers to the fact that the probability of selecting any particular individual is not influenced by the individuals already selected for the sample.
if more than one individual is being selected, the probabilities must stay constant from one selection to the next.
We will typically omit the word “independent” and simply refer to this sampling technique as random sampling. you should always assume that both requirements (equal chance and constant probability) are part of the selection process.
For a situation in which several different outcomes are possible, the probability for any specific outcome is defined as a fraction or a proportion of all the possible outcomes.
we use proportions to summarize previous observations, and probability is used to predict future, uncertain outcomes.
The probability of a specific outcome is expressed with a p (for probability), followed by the specific outcome in parentheses.
Note that probability is defined as a proportion, or a part of the whole.
Extremes
At the other extreme, when an event always occurs, the probability is 1, or 100%.
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At one extreme, when an event never occurs, the probability is zero, or 0%.
Probabilities, Proportions, and z-Scores
The unit normal table can be used only with normal-shaped distributions. If a distribution is not normal, transforming X values to z-scores will not make it normal.
Transform the X values into z-scores.
Use the unit normal table to look up the proportions corresponding to the z-score values.
To keep the probabilities from changing from one selection to the next, it is necessary to return each individual to the population before you make the next selection. This process is called sampling with replacement. The second requirement for random samples (constant probability) demands that you sample with replacement.
Finding Percentiles
finding an X value from a percentage requires the intermediate step of determining the z-score for that proportion of the distribution.
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When population data form a normal distribution there is a simple method to compute the interquartile range from the unit normal table.
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