note cards 5.1-5.5 - Section 5.1 P roperties of a Normal D...

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Section 5.1 Properties of a Normal Distribution Guidelines A normal distribution is a continuous probability distribution for a random variable x. The graph of a normal distribution is called the normal curve. A normal distribution has the following properties. 1. The mean, median, and mode are equal. 2. The normal curve is bell-shaped and is symmetric about the mean.
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3. The total area under the normal curve is equal to one. 4. The normal curve approached, but never touches, the x- axis as it extends farther and farther away from the mean. 5. Between - + μ σ and μ σ (in the center of the curve), the graph curves downward. The graph curves upward to the left of - μ σ and to the right of + μ σ . The points at which the curve changes from curving upward to curving downward are called inflection points .
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Probability density function (pdf) = = -( - ) / y 1σ2πe x μ 2 2σ2 e= 2.718 and = 3.14 σ is the from one inflection point to the mean Y= 2 nd DISTR
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1:normalpdf( Enter x and the values of u and σ seperated by commas. GRAPH The Standard normal distribution The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1.
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Properties of the Standard Normal Distribution 1. The cumulative area is close to 0 for z-scores close to z= -3.49. 2. The cumulative area increases as the z-scores increase.
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