1. Chapter 5 The Normal Curve and Standard Scores EPS 525 Introduction to Statistics

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3. Raw Score (IQ): 52 68 84 100 116 132 148

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

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

10. What is the proportion of scores in a normal distribution between z = -0.19 and z = +3.02? Therefore, the Area of Interest = 7.53 + 49.87 = 57.40% Area A = 7.53% (and) Area B = 49.87%

11. What is the proportion of scores in a normal distribution between z = +0.19 and z = +1.12? Therefore, the Area of Interest* = 36.86 - 7.53 = 29.33% Area A = 7.53% (and) Area B (total) = 36.86%

13. What is the proportion of scores in a normal distribution between z = -1.09 and z = -3.02? Therefore, the Area of Interest* = 49.87 – 36.21 = 13.66% Area A = 36.21% (and) Area B (total) = 49.87%

14. 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 = 50.00 – 30.78 = 19.22%

15. 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 = 50.00 + 39.97 = 89.97%

16. 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 = 50.00 + 47.72 = 97.72%

17. 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 = 50.00 – 19.85 = 30.15%

18. Knowing that the mean is 50 and s = 3, what are the raw scores that bound the middle 39% of the normal distribution? Using Table A – we find that z = +.51 will bound the middle 39% of the scores. Area Between Mean and z =.1950 (39/2 =.1950) -.51.51 Solve for the lower X:Solve for the upper X: Therefore, the two raw scores that bound the middle 39% are 48.47 and 51.53 48.47 51.53