A variable is said to be normally distributed or to have a normal distribution if its distribution has the shape of a normal curve Cheap Pittsburgh Penguins Jerseys , a special type of bell-shaped curve. Theoretically, a density curve represents the distribution of a continuous variable. However, a density curve can often be used to approximate the distribution of a discrete variable. Two basic properties of every density curve are as follows.

• Property 1: A density curve is always on or above the horizontal axis. • Property 2: The total area under a density curve (and above the horizontal axis) equals 1.

One of the most important uses of the density curve of a variable relies on the fact that percentages for the variable are equal to areas under its density curve. A normal distribution (and hence a normal curve) is completely determined by the mean and standard deviation; that is, two normally distributed variables having the same mean and standard deviation must have the same distribution. We often identify a normal curve by stating the corresponding mean and standard deviation and calling those the parameters of the normal curve. A normal distribution is symmetric about and centered at the mean of the variable, and its spread depends on the standard deviation of the variable—the larger the standard deviation Cheap Philadelphia Flyers Jerseys , the flatter and more spread out is the distribution.

How do we find areas under a normal curve? Conceptually, we need a table of areas for each normal curve. This, of course, is impossible because there are infinitely many different normal curves—one for each choice of μ and σ. The way out of this difficulty is standardizing, which transforms every normal distribution into one particular normal distribution Cheap Ottawa Senators Jerseys , the standard normal distribution. A normally distributed variable having mean 0 and standard deviation 1 is said to have the standard normal distribution. Its associated normal curve is called the standard normal curve. The standardized version of any variable has mean 0 and standard deviation 1. A normally distributed variable furthermore has a normally distributed standardized version. Consequently, for a normally distributed variable, we can find the percentage of all possible observations that lie within any specified range by

• Expressing the range in terms of z-scores, and • Determining the corresponding area under the standard normal curve.

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