Homework 4-chapter 5-6 Normality

Homework 4-Chapters 5 & 6 normality 1. Report the percentage of values that falls between the mean of a given set of data and a Z score of +0.89. 31.33% 2. Given a set of data with a mean of 35.1 and a standard deviation of 7.8, calculate the Z score equivalents of the following raw scores: (a) 21.6, (b) 43.3, (c) 8.8, and (d) 68.5. What is the interpretation of the Z scores? X Mean Z Calculations: a. 21.6 35.1 -1.731 (21.6-35.1)/7.8 b. 43.3 1.0513 (43.3-35.1)/7.8 c. 8.8 SD -3.372 (8.8-35.1)/7.8 d. 68.5 7.8 4.282 (685-35.1)/7.8 3. Use table A.1 in appendix A (p. 314-315) to determine the equivalent percentile rank of each of the scores in problem #2. X Mean % rank a. 21.6 35.1 4.18 b. 43.3 85.31 c. 8.8 SD 0.04 d. 68.5 7.8 100 4. ¯ X = ∑ X N You have collected the following data for 1.5 mile run times (X) from twelve (N=12) KU students. σ = √ Σ ( x − x ) 2 N Sub. 1.5 mile run time (min) (X) X 2 1 8.230 67.7329 2 11.908 141.8005 3 13.560 183.8736 4 7.020 49.2804 5 11.380 129.5064 The Z-score represents how many standard deviations the number is from the mean. Z = X −¯ X SD

6 11.830 139.3489 7 10.290 105.8841 8 9.210 84.8241 9 9.820 96.4324 10 8.550 73.1025 11 10.910 119.0281 12 10.300 106.0900 a. Calculate the mean and standard deviation (σ) for 1.5 mile run times Mean = 10.251 minutes SD = 1.7442 minutes 5. You have collected the following data for VO 2 max (Y) from twelve (N=12) KU students. ¯ X = ∑ X N Sub. VO 2 max (ml·kg -1 ·min -1 ) (Y) Y 2 1 49.210 2421.6241 2 32.030 1025.7207 3 28.560 815.6736 4 52.420 2141.8564 5 36.360 1322.0496 6 35.120 1233.4144 7 38.880 1511.6544 8 42.350 1793.5225 9 40.200 1616.04 10 45.230 2045.7529 11 38.260 1463.8276 12 39.590 1567.3681 a. Calculate the mean and standard deviation (σ) for VO 2 max mean = 39.85083 SD = 6.5041 6. Calculate the skewness and kurtosis statistics for VO 2 max and 1.5 mile run times and interpret the shapes of their frequency distributions (skewness, kurtosis, SE skew , SE kurt , Z skew , Z kurt )

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