In the following examples, the mean time it takes expectant mothers to locate a baby face in a crowd is 77 milliseconds. There is a standard deviation of 10 milliseconds for the recognition of the babies faces. What proportion of expectant mothers took an average of 90 (X=90) milliseconds or less to recognize the babies faces?

The previous example demonstrated finding the probability of observing a known X value. We started with an X value found the corresponding Z-score and used the Z-table to find the probability. We can also find raw scores for certain percentages of the population (working the problem in reverse order). Perhaps we know the mean and standard deviation of a population, for example, and want to find the raw score that corresponds to a certain percentage of the distribution. Now we start with the probability, find the Z-value and solve for X.

In the following example the average miles per gallon (MPG) a Ford motor car gets is 23 with a standard deviation of 5. How many miles to the gallon does the top 10% of Ford cars get?