5: Normal Probability Distribution
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- 5.1: The Standard Normal Distribution
- A z-score is a standardized value. Its distribution is the standard normal, Z∼N(0,1). The mean of the z-scores is zero and the standard deviation is one. If y is the z-score for a value x from the normal distribution N(μ,σ) then z tells you how many standard deviations x is above (greater than) or below (less than) μ.
- 5.2: Area Under Any Normal Curve
- The normal distribution, which is continuous, is the most important of all the probability distributions. Its graph is bell-shaped. This bell-shaped curve is used in almost all disciplines. Since it is a continuous distribution, the total area under the curve is one. The parameters of the normal are the mean μ and the standard deviation σ. A special normal distribution, called the standard normal distribution is the distribution of z-scores. Its mean is zero, and its standard deviation is one.