Example 1.39

EXAMPLE 1.39 How High for the Top 10%?

Scores on the SAT Verbal test in recent years follow approximately the distribution. How high must a student score be for it to place in the top 10% of all students taking the SAT?

Again, the key to the problem is to draw a picture. Figure 1.27 shows that we want the score with area above it to be 0.10. That’s the same as area below equal to 0.90.

Statistical software has a function that will give you the for any cumulative proportion you specify. The function often has a name such as “inverse cumulative probability.” Plug in mean 505, standard deviation 110, and cumulative proportion 0.9. The software tells you that . We see that a student must score at least 646 to place in the highest 10%.

Figure 1.29: FIGURE 1.27 Locating the point on a Normal curve with area 0.10 to its right, Example 1.39. The result is , or in the standard scale.