• Step 1 Determine , , and .

  We have already seen that has mean and standard deviation . Once again, draw a graph of the distribution of scores , with the mean 514 in the middle, the score 215 to the left of the mean, and the score 595 to the right of the mean, as in Figure 50.

• Step 2 Standardize.

  This is a “between” example, where two values of are given, and we are asked to find the area between them. In this case, just standardize both of these values of to get a -value for each:

  

  Figure 6.52: FIGURE 50 Graph of percentage of students scoring between 215 and 595 on the Math SAT.

• Step 3 Draw the standard normal curve.

  Draw a graph of , shading the area between and , as shown in Figure 51. Again, the key is that the area between and is exactly the same as the area between and .

• Step 4 Find area under the standard normal curve.

  Figure 51 is a Case 3 problem from Table 8 (page 355). Find the area to the left of 0.69, which is 0.7549, and the area to the left of −2.53, which is 0.0057. Subtracting the smaller from the larger gives us

  Thus, the percentage of Math SAT scores that are between 215 and 595 is 74.92%.

  

  Figure 6.53: FIGURE 51 Graph of percentage of - values between −2.53 and 0.69.

NOW YOU CAN DO