Chapter 4 The Normal Distribution EPS 625 Statistical Methods Applied to Education I

Figure 4.3, page 85

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What is the proportion of scores in a normal distribution between the mean and z = +0.52? Answer: 19.85%

What is the proportion of scores in a normal distribution between the mean and z = -1.89? Answer: 47.06%

What is the proportion of scores in a normal distribution between z = and z = +3.02? Therefore, the Area of Interest = = 57.40% Area A = 7.53% (and) Area B = 49.87%

What is the proportion of scores in a normal distribution between z = and z = +1.12? Therefore, the Area of Interest* = = 29.33% Area A = 7.53% (and) Area B (total) = 36.86%

What is the proportion of scores in a normal distribution between z = and z = -3.02? Therefore, the Area of Interest* = – = 13.60% Area A = 36.27% (and) Area B (total) = 49.87%

What is the proportion of scores in a normal distribution above z = +0.87? Area A (total beyond z = 0.00) = 50.00% (and) Area B = 30.78% Or – use “Area Beyond z” Column Locate z = 0.87 and you will find 19.22% Therefore, the Area of Interest = – = 19.22%

What is the proportion of scores in a normal distribution below z = +1.28? We know that Area A (total beyond z = 0.00) = 50.00% We find Area B = 39.97% Therefore, the Area of Interest = = 89.97%

What is the proportion of scores in a normal distribution above z = -2.00? We know that Area B (total beyond z = 0.00) = 50.00% We find Area A = 47.72% Therefore, the Area of Interest = = 97.72%

What is the proportion of scores in a normal distribution below z = -0.52? Area A = 19.85% (and) Area B (total beyond z = 0.00) = 50.00% Or – use “Area Beyond z” Column Locate z = 0.52 and you will find 30.15% Therefore, the Area of Interest = – = 30.15%