Nonstandard Distributions
Converting Nonstandard Distributions
Create a bell-shaped curve with the nonstardard values and indicate the mean and stardard deviation.
Convert each critical value into their Z score. Isolate z from: x = u +z*sigma
Find the area of the area under the normal distribution using a calculator or book table.
Z scores
This is a distance on the x axis of the normal distribution meaning the standard deviations that any value is from the mean.
In statistics we say: The area value of 0.9306 that there is a probability of 0.9306 or 93.06% of randomly selecting a z score less than 1.48.
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Probabilities for Normal Distributions
This is also known as the area under the curve or relative frequency. This area should be equal to 1.
Ways to express areas under the bell-shaped curve.
- P ( a < z < b) for z values between a and b.
- P ( z > a) for z values greater than b.
- P ( z < a ) for z values smaller than a.
Critical Values
This is a z score to separate the area from the left to the right. Tables on books shows cumulative area from the left up to this z value.
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