In order to use the area of the normal curve to determine the probability of occurrence of a given value, the value must first be standardized, or converted to a z-score . To convert a value to a z-score is to express it in terms of how many standard deviations it is above or below the mean. After the z-score is obtained, you can look up its corresponding probability in a table. The formula to compute a z-score is where x is the value to be converted, μ is the population mean, and is the population standard σ deviation. Example 1 A normal distribution of retail-store purchases has a mean of $14.31 and a standard deviation of 6.40. What percentage of purchases were under $10? First, compute the z-score: The next step is to look up the z-score in the table of standard normal probabilities (see Table 2 in "Statistics Tables"). The standard normal table lists the probabilities (curve areas) associated with
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