In order to use the area of the normal curve to determine the probability of occurrence of a given v

# In order to use the area of the normal curve to determine the probability of occurrence of a given v

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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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