EXAMPLE 1.37 Find the Proportion from X

What proportion of all students who take the SAT have scores of at least 820? The picture that leads to the answer is exactly the same as in Example 1.34 (pages 46-47). The extra step is that we first standardize in order to read cumulative proportions from Table A. If is SAT score, we want the proportion of students for whom .

Step 1. Standardize. Subtract the mean, then divide by the standard deviation, to transform the problem about into a problem about a standard Normal Z:

Step 2. Use the table. Look at the pictures in Example 1.34. From Table A, we see that the proportion of observations less than -0.99 is 0.1611. The area to the right of -0.99 is, therefore, . This is about 84%.