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Probability - mathematical study of chance, calculating how likely…
Probability - mathematical study of chance, calculating how likely specific events are to occur. Statistics is the application of mathematical models to collect, analyze, and interpret real-world data.
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p-Value (Probability Value) - statistical measure used to determine if the results of an experiment or study are meaningful rather than just occurring by random chance.
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Unit Normal Table (z-Table) - a mathematical reference in statistics that provides the probabilities (areas under the curve) of a standard normal distribution.
The normal distribution is symmetrical, the proportions on the right-hand side are exactly the same as the corresponding proportions on the left-hand side.
The table does not list negative z-score values. To find proportions for negative z-scores, you must look up the corresponding proportions for the positive value of z
All frequency distributions, probability questions can be answered by determining proportions of area. The “probability of selecting an individual with an IQ greater than 108” is equivalent to the “proportion of the whole population that consists of IQs greater than 108.”
The z-score values change signs (+ and −) from one side to the other; however, the proportions are always positive. Column C in the table always lists the proportion in the tail whether it is the right-hand or left-hand tail.
- Transform the X values into z-scores. 2. Use the unit normal table to look up the proportions corresponding to the z-score values.
A standard table is broken down by the z-score (usually rounded to the nearest hundredth) on the axes, corresponding to distinct regions of the normal curve.
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Percentile Rank - the percentage of individuals in the distribution with scores at or below that particular score.
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Quartiles - scores having percentile ranks of 25%, 50%, 75%, and 100%, termed the 1st, 2nd, 3rd, and 4th quartile.
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For a normal distribution, the first quartile always corresponds to z = -0.67, the second quartile corresponds to z = 0 (the mean), and the third quartile corresponds to z = +0.67.
Because a percentile rank is the percentage of the individuals who fall below a particular score, we will need to find the proportion of the distribution to the left of the score. When finding percentile ranks, we will always be concerned with the percentage on the left-hand side of an X value. Therefore, if the X value is above the mean, the proportion to the left will be found in column B (the body of the distribution) of the unit normal table.
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