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Section 1.3

Section 1.3 - 1 SECTION 1.3 THE NORMAL DISTRIBUTION DENSITY...

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Unformatted text preview: 1 SECTION 1.3 - THE NORMAL DISTRIBUTION DENSITY CURVES A density curve is a curve that • Is always on or above the horizontal axis • Has area exactly 1 underneath it • Describes the overall pattern of a distribution. The area under the density curve and above any range of values is the relative frequency of all observation that fall in that range. Physical Interpretation • The mean of a density curve is the point at which the curve would balance if made of solid material. • The median of a density curve is the point that divides the area under the curve in half. THE NORMAL DISTRIBUTION Normal curves are an important class of curves which have the following properties: • They are symmetric, bell-shaped, unimodal. • The mean and median are always in the center of the graph (and they are equal). • The standard deviation controls the spread of a normal curve (where curve changes concavity). • Changing the mean moves the normal curve along the horizontal axis. • The normal curve is completely determined by and . • The distribution is abbreviated N( , ). • Probabilities are areas under the normal curve between the points of interest. THE 68-95-99.7 RULE In the normal distribution with mean and standard deviation : • Approximately 68% of the observations fall within of the mean . • Approximately 95% of the observations fall within 2 of . • Approximately 99.7% of the observations fall within 3 of . 2 EXAMPLE (From Moore and McCabe - fifth edition) Bigger animals tend to carry their young longer before birth. The length of horse pregnancies from conception to birth varies according to a roughly normal distribution with mean 336 days and standard deviation 3 days. Use the 68-95-99.7 rule to answer the following questions....
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Section 1.3 - 1 SECTION 1.3 THE NORMAL DISTRIBUTION DENSITY...

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