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Normal Approximation to the Binomial

# Normal Approximation to the Binomial - either fall through...

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Normal Approximation to the Binomial Some variables are continuous—there is no limit to the number of times you could  divide their intervals into still smaller ones, although you may round them off for  convenience. Examples include age, height, and cholesterol level. Other variables are  discrete, or made of whole units with no values between them. Some discrete variables  are the number of children in a family, the sizes of televisions available for purchase, or  the number of medals awarded at the Olympic Games.  A binomial variable can take only two values, often termed  successes  and  failures Examples include coin tosses that come up either heads or tails, manufactured parts  that either continue working past a certain point or do not, and basketball tosses that
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Unformatted text preview: either fall through the hoop or do not. You discovered that the outcomes of binomial trials have a frequency distribution, just as continuous variables do. The more binomial trials there are (for example, the more coins you toss simultaneously), the more closely the sampling distribution resembles a normal curve (see Figure 1). You can take advantage of this fact and use the table of standard normal probabilities (Table 2 in "Statistics Tables") to estimate the likelihood of obtaining a given proportion of successes. You can do this by converting the test proportion to a z-score and looking up its probability in the standard normal table....
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