12.5 The Normal Curve 815 c) When determining the area to the right of a z-score, subtract the percent of data to the left of the specified z-score from 100%. 0 z – = Area under entire curve = 1.0000 0 Area to the left of z Area to the right of z 0 z Or, use the symmetry of a normal distribution. 0 z z = Area to the left of z (z < 0) 0 Area to the right of z (z > 0) d) When determining the area between two z-scores, subtract the smaller area from the larger area. In the figure below, we let z1 represent the smaller z-score and z2 represent the larger z-score. – = Area to the left of z2 Area between z1 and z2 0 Area to the left of z1 z2 0 z1 0 z1 z2 4. Change the areas you determined in Step 3 to percents as explained on page 814. Example 3 IQ Scores Intelligence quotients (IQ scores) are normally distributed with a mean of 100 and a standard deviation of 15. Determine the percent of individuals with IQ scores a) below 115. b) below 130. c) below 70. d) between 70 and 115. e) between 115 and 130. f) above 122.5. Solution a) We want to determine the area under the normal curve below the value of 115, as illustrated in Fig. 12.30(a). Converting 115 to a z-score yields a z-score of 1.00. = − = = z 115 100 15 15 15 1.00 115 100 (a) 115 Original values 0 (b) 1.00 z-scores 84.13% Figure 12.30
RkJQdWJsaXNoZXIy NjM5ODQ=