Appendix A: Areas under the standard normal curve
(mean =0, standard deviation = 1)
Area Area Area Area
between Area between Area between Area between
Mean and beyond Mean beyond Mean beyond Mean Area
Z Z Z Z and Z Z Z and Z Z Z and Z beyond Z
0.00 0.00 50.00 0.51 19.50 30.50 1.02 34.61 15.39 1.53 43.70 6.30
0.01 0.40 49.60 0.52 19.85 30.15 1.03 34.85 15.15 1.54 43.82 6.18
0.02 0.80 49.20 0.53 20.19 29.81 1.04 35.08 14.92 1.55 43.94 6.06
0.03 1.20 48.80 0.54 20.54 29.46 1.05 35.31 14.69 1.56 44.06 5.94
0.04 1.60 48.40 0.55 20.88 29.12 1.06 35.54 14.46 1.57 44.18 5.82
0.05 1.99 48.01 0.56 21.23 28.77 1.07 35.77 14.23 1.58 44.29 5.71
0.06 2.39 47.61 0.57 21.57 28.43 1.08 35.99 14.01 1.59 44.41 5.59
0.07 2.79 47.21 0.58 21.90 28.10 1.09 36.21 13.79 1.60 44.52 5.48
0.08 3.19 46.81 0.59 22.24 27.76 1.10 36.43 13.57 1.61 44.63 5.37
0.09 3.59 46.41 0.60 22.57 27.43 1.11 36.65 13.35 1.62 44.74 5.26
0.10 3.98 46.02 0.61 22.91 27.09 1.12 36.86 13.14 1.63 44.84 5.16
0.11 4.38 45.62 0.62 23.24 26.76 1.13 37.08 12.92 1.64 44.95 5.05
0.12 4.78 45.22 0.63 23.57 26.43 1.14 37.29 12.71 1.65 45.05 4.95
0.13 5.17 44.83 0.64 23.89 26.11 1.15 37.49 12.51 1.66 45.15 4.85
0.14 5.57 44.43 0.65 24.22 25.78 1.16 37.70 12.30 1.67 45.25 4.75
0.15 5.96 44.04 0.66 24.54 25.46 1.17 37.90 12.10 1.68 45.35 4.65
0.16 6.36 43.64 0.67 24.86 25.14 1.18 38.10 11.90 1.69 45.45 4.55
0.17 6.75 43.25 0.68 25.17 24.83 1.19 38.30 11.70 1.70 45.54 4.46
0.18 7.14 42.86 0.69 25.49 24.51 1.20 38.49 11.51 1.71 45.64 4.36
0.19 7.53 42.47 0.70 25.80 24.20 1.21 38.69 11.31 1.72 45.73 4.27
0.20 7.93 42.07 0.71 26.11 23.89 1.22 38.88 11.12 1.73 45.82 4.18
0.21 8.32 41.68 0.72 26.42 23.58 1.23 39.07 10.93 1.74 45.91 4.09
0.22 8.71 41.29 0.73 26.73 23.27 1.24 39.25 10.75 1.75 45.99 4.01
0.23 9.10 40.90 0.74 27.04 22.96 1.25 39.44 10.56 1.76 46.08 3.92
0.24 9.48 40.52 0.75 27.34 22.66 1.26 39.62 10.38 1.77 46.16 3.84
0.25 9.87 40.13 0.76 27.64 22.36 1.27 39.80 10.20 1.78 46.25 3.75
0.26 10.26 39.74 0.77 27.94 22.06 1.28 39.97 10.03 1.79 46.33 3.67
0.27 10.64 39.36 0.78 28.23 21.77 1.29 40.15 9.85 1.80 46.41 3.59
0.28 11.03 38.97 0.79 28.52 21.48 1.30 40.32 9.68 1.81 46.49 3.51
0.29 11.41 38.59 0.80 28.81 21.19 1.31 40.49 9.51 1.82 46.56 3.44
0.30 11.79 38.21 0.81 29.10 20.90 1.32 40.66 9.34 1.83 46.64 3.36
0.31 12.17 37.83 0.82 29.39 20.61 1.33 40.82 9.18 1.84 46.71 3.29
0.32 12.55 37.45 0.83 29.67 20.33 1.34 40.99 9.01 1.85 46.78 3.22
0.33 12.93 37.07 0.84 29.95 20.05 1.35 41.15 8.85 1.86 46.86 3.14
0.34 13.31 36.69 0.85 30.23 19.77 1.36 41.31 8.69 1.87 46.93 3.07
0.35 13.68 36.32 0.86 30.51 19.49 1.37 41.47 8.53 1.88 46.99 3.01
0.36 14.06 35.94 0.87 30.78 19.22 1.38 41.62 8.38 1.89 47.06 2.94
0.37 14.43 35.57 0.88 31.06 18.94 1.39 41.77 8.23 1.90 47.13 2.87
0.38 14.80 35.20 0.89 31.33 18.67 1.40 41.92 8.08 1.91 47.19 2.81
0.39 15.17 34.83 0.90 31.59 18.41 1.41 42.07 7.93 1.92 47.26 2.74
0.40 15.54 34.46 0.91 31.86 18.14 1.42 42.22 7.78 1.93 47.32 2.68
0.41 15.91 34.09 0.92 32.12 17.88 1.43 42.36 7.64 1.94 47.38 2.62
0.42 16.28 33.72 0.93 32.38 17.62 1.44 42.51 7.49 1.95 47.44 2.56
0.43 16.64 33.36 0.94 32.64 17.36 1.45 42.65 7.35 1.96 47.50 2.50
0.44 17.00 33.00 0.95 32.89 17.11 1.46 42.79 7.21 1.97 47.56 2.44
0.45 17.36 32.64 0.96 33.15 16.85 1.47 42.92 7.08 1.98 47.61 2.39
0.46 17.72 32.28 0.97 33.40 16.60 1.48 43.06 6.94 1.99 47.67 2.33
0.47 18.08 31.92 0.98 33.65 16.35 1.49 43.19 6.81 2.00 47.72 2.28
0.48 18.44 31.56 0.99 33.89 16.11 1.50 43.32 6.68 2.01 47.78 2.22
0.49 18.79 31.21 1.00 34.13 15.87 1.51 43.45 6.55 2.02 47.83 2.17
0.50 19.15 30.85 1.01 34.38 15.62 1.52 43.57 6.43 2.03 47.88 2.12
(mean =0, standard deviation = 1)
Area Area Area Area
between Area between Area between Area between
Mean and beyond Mean beyond Mean beyond Mean Area
Z Z Z Z and Z Z Z and Z Z Z and Z beyond Z
0.00 0.00 50.00 0.51 19.50 30.50 1.02 34.61 15.39 1.53 43.70 6.30
0.01 0.40 49.60 0.52 19.85 30.15 1.03 34.85 15.15 1.54 43.82 6.18
0.02 0.80 49.20 0.53 20.19 29.81 1.04 35.08 14.92 1.55 43.94 6.06
0.03 1.20 48.80 0.54 20.54 29.46 1.05 35.31 14.69 1.56 44.06 5.94
0.04 1.60 48.40 0.55 20.88 29.12 1.06 35.54 14.46 1.57 44.18 5.82
0.05 1.99 48.01 0.56 21.23 28.77 1.07 35.77 14.23 1.58 44.29 5.71
0.06 2.39 47.61 0.57 21.57 28.43 1.08 35.99 14.01 1.59 44.41 5.59
0.07 2.79 47.21 0.58 21.90 28.10 1.09 36.21 13.79 1.60 44.52 5.48
0.08 3.19 46.81 0.59 22.24 27.76 1.10 36.43 13.57 1.61 44.63 5.37
0.09 3.59 46.41 0.60 22.57 27.43 1.11 36.65 13.35 1.62 44.74 5.26
0.10 3.98 46.02 0.61 22.91 27.09 1.12 36.86 13.14 1.63 44.84 5.16
0.11 4.38 45.62 0.62 23.24 26.76 1.13 37.08 12.92 1.64 44.95 5.05
0.12 4.78 45.22 0.63 23.57 26.43 1.14 37.29 12.71 1.65 45.05 4.95
0.13 5.17 44.83 0.64 23.89 26.11 1.15 37.49 12.51 1.66 45.15 4.85
0.14 5.57 44.43 0.65 24.22 25.78 1.16 37.70 12.30 1.67 45.25 4.75
0.15 5.96 44.04 0.66 24.54 25.46 1.17 37.90 12.10 1.68 45.35 4.65
0.16 6.36 43.64 0.67 24.86 25.14 1.18 38.10 11.90 1.69 45.45 4.55
0.17 6.75 43.25 0.68 25.17 24.83 1.19 38.30 11.70 1.70 45.54 4.46
0.18 7.14 42.86 0.69 25.49 24.51 1.20 38.49 11.51 1.71 45.64 4.36
0.19 7.53 42.47 0.70 25.80 24.20 1.21 38.69 11.31 1.72 45.73 4.27
0.20 7.93 42.07 0.71 26.11 23.89 1.22 38.88 11.12 1.73 45.82 4.18
0.21 8.32 41.68 0.72 26.42 23.58 1.23 39.07 10.93 1.74 45.91 4.09
0.22 8.71 41.29 0.73 26.73 23.27 1.24 39.25 10.75 1.75 45.99 4.01
0.23 9.10 40.90 0.74 27.04 22.96 1.25 39.44 10.56 1.76 46.08 3.92
0.24 9.48 40.52 0.75 27.34 22.66 1.26 39.62 10.38 1.77 46.16 3.84
0.25 9.87 40.13 0.76 27.64 22.36 1.27 39.80 10.20 1.78 46.25 3.75
0.26 10.26 39.74 0.77 27.94 22.06 1.28 39.97 10.03 1.79 46.33 3.67
0.27 10.64 39.36 0.78 28.23 21.77 1.29 40.15 9.85 1.80 46.41 3.59
0.28 11.03 38.97 0.79 28.52 21.48 1.30 40.32 9.68 1.81 46.49 3.51
0.29 11.41 38.59 0.80 28.81 21.19 1.31 40.49 9.51 1.82 46.56 3.44
0.30 11.79 38.21 0.81 29.10 20.90 1.32 40.66 9.34 1.83 46.64 3.36
0.31 12.17 37.83 0.82 29.39 20.61 1.33 40.82 9.18 1.84 46.71 3.29
0.32 12.55 37.45 0.83 29.67 20.33 1.34 40.99 9.01 1.85 46.78 3.22
0.33 12.93 37.07 0.84 29.95 20.05 1.35 41.15 8.85 1.86 46.86 3.14
0.34 13.31 36.69 0.85 30.23 19.77 1.36 41.31 8.69 1.87 46.93 3.07
0.35 13.68 36.32 0.86 30.51 19.49 1.37 41.47 8.53 1.88 46.99 3.01
0.36 14.06 35.94 0.87 30.78 19.22 1.38 41.62 8.38 1.89 47.06 2.94
0.37 14.43 35.57 0.88 31.06 18.94 1.39 41.77 8.23 1.90 47.13 2.87
0.38 14.80 35.20 0.89 31.33 18.67 1.40 41.92 8.08 1.91 47.19 2.81
0.39 15.17 34.83 0.90 31.59 18.41 1.41 42.07 7.93 1.92 47.26 2.74
0.40 15.54 34.46 0.91 31.86 18.14 1.42 42.22 7.78 1.93 47.32 2.68
0.41 15.91 34.09 0.92 32.12 17.88 1.43 42.36 7.64 1.94 47.38 2.62
0.42 16.28 33.72 0.93 32.38 17.62 1.44 42.51 7.49 1.95 47.44 2.56
0.43 16.64 33.36 0.94 32.64 17.36 1.45 42.65 7.35 1.96 47.50 2.50
0.44 17.00 33.00 0.95 32.89 17.11 1.46 42.79 7.21 1.97 47.56 2.44
0.45 17.36 32.64 0.96 33.15 16.85 1.47 42.92 7.08 1.98 47.61 2.39
0.46 17.72 32.28 0.97 33.40 16.60 1.48 43.06 6.94 1.99 47.67 2.33
0.47 18.08 31.92 0.98 33.65 16.35 1.49 43.19 6.81 2.00 47.72 2.28
0.48 18.44 31.56 0.99 33.89 16.11 1.50 43.32 6.68 2.01 47.78 2.22
0.49 18.79 31.21 1.00 34.13 15.87 1.51 43.45 6.55 2.02 47.83 2.17
0.50 19.15 30.85 1.01 34.38 15.62 1.52 43.57 6.43 2.03 47.88 2.12