Normal Distributions

Normal DistributionsSo far we have dealt with random variables with a finitenumber of possible values. For example; ifXis the numberof heads that will appear, when you flip a coin 5 times,Xcan only take the values 0,1,2,3,4,or variables can take a continuous range of values, forexample a variable such as the height of 2 year old childrenin the population or the lifetime of an electroniccomponent. For a continuous random variableX, theanalogue of a histogram is a continuous curve (theprobability density function) and it is our primary tool infinding probabilities related to the variable. As with thehistogram for a random variable with a finite number ofvalues, the total area under the curve equals DistributionsProbabilities correspond to areas under the curve and arecalculated over intervals rather than for specific values ofthe random many types of probability density functionscommonly occur, we will restrict our attention to randomvariables with Normal Distributions and the probabilitieswill correspond to areas under aNormal Curve(ornormal density function).

The standard Normal curve is the normal curve with mean = 0 and standard deviation ˙= 1. We will see later how probabilities for any normal curve can be recast as probabilities for the standard normal curve. For the standard normal, probabilities are computed either by means of a computer/calculator of via a table.

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  Name, Standards, Deviation, And standard deviation

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