Basic Statistics for Business and Economics ch 7
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| What are the two families of continuous probability distributions? | Uniform probability distribution and normal probability distribution.
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| Uniform Probability Distribution | The simplest distribution for a continuous random variable. This distribution is rectangular in shape and is defined by minimum and maximum values.
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| Mean of the Uniform Distribution (mu) = | (a + b)/2
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| Standard Deviation of the Uniform Distribution (sigma) = | The square root of [(b-a)^2]/12
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| Uniform Distribution P(X) = | 1/(b-a) [if x is between or equal to a and b]
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| Area = | Height * Base
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| What are the characteristics of a normal probability distribution? | It is bell-shaped and had a single peak at the center of the distribution. It is symmetrical about the mean. It falls off smoothly in either direction for the central values - it is asymptotic. Location of a normal distribution is determined by the mean.
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| Bell-Shaped | The arithmetic mean, median, and mode are equal and located in the center of the distribution. The total are under the curve is 1.00. Half of the area under the normal curve is to the right of the center and the other half is to the left of it.
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| Symmetrical | If the normal curve is cut vertically at the center value, the two halves will be mirror images.
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| Asymptotic | The curve gets closer and closer to the X-axis but never actually touches it. The tails of the curve extend indefinitely in both directions.
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| The dispersion or spread of the distribution is determined by: | The standard deviation (sigma).
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| Standard Normal Probability Distribution | One member of the family of normal distributions that can be used to determine the probabilities for all normal distributions. It is unique because it has a mean of 0 and a standard deviation of 1.
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| z Value | The signed distance between a selected value, designated X, and the mean (mu), divided by the standard deviation (sigma).
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| Empirical Rule | For symmetrical bell-shaped frequency distribution about 68% of the observations will lie within plus and minus 1 standard deviation of the mean; 95% of the observations will lie within 2 standard deviations, and 99.7% within 3 standard deviations.
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