43. Chebyshev's Theorem Based on Data Set 1 “Body Data" in Appendix B, blood platelet counts of women have a bell-shaped distribution with a mean of 255.1 and a standard deviation of 65.4. (All units are 1000 cells/µL.) Using Chebyshev's theorem, what do we know about the percentage of women with platelet counts that are within 3 standard deviations of the mean? What are the minimum and maximum platelet counts that are within 3 standard deviations of the mean? Data Set 1: Body Data (1000 cells/uL), RED is red blood cell count (million cells/uL), Body and exam measurements are from 300 subjects (first five rows shown here). AGE is in years, for GENDER I = male and 0 = female, PULSE is pulse rate (beats per minute), SYSTOLIC is systolic blood pressure (mm Hg), DIASTOLIC is diastolic blood pressure (mm Hg), HDL is HDL cholesterol (mg/dL), LDL is LDL cholesterol (mg/dL). WHITE is white blood cell count PLATE is platelet count (1000 cells/uL), WEIGHT is weight (kg), HEIGHT is height (cm), WAIST is waist circumference (cm), ARM CIRC is arm circumference (cm), and BMI is body mass index (kg/m2). Data are from the National Center for Health Statistics. TI-83/84 list names AGE, GENDR, PULSE, SYS, DIAS, HDL, (BODY): LDL, WHITE, REDBC, PLATE, WT, HT, WAIST, ARMC, BMI AGE GENDER (1 = M) PULSE SYSTOLIC DIASTOLIC HDL LDL WHITE RED PLATE WEIGHT HEIGHT WAIST ARM CIRC BMI %3D 43 80 100 70 73 68 8.7 4.80 319 98.6 172.0 120.4 40.7 33.3 57 1 84 112 70 35 116 4.9 4.73 187 96.9 186.0 107.8 37.0 28.0 38 94 134 94 36 223 6.9 4.47 297 108.2 154.4 120.3 44.3 45.4 80 1 74 126 64 37 83 7.5 4.32 170 73.1 160.5 97.2 30.3 28.4 34 1 50 114 68 50 104 6.1 4.95 140 83.1 179.0 95.1 34.0 25.9 43. At least 89% of women have platelet counts within 3 standard deviations of the mean. The minimum is 58.9 and the maximum is 451.3.

# 43. Chebyshev's Theorem Based on Data Set 1 “Body Data" in Appendix B, blood platelet counts of women have a bell-shaped distribution with a mean of 255.1 and a standard deviation of 65.4. (All units are 1000 cells/µL.) Using Chebyshev's theorem, what do we know about the percentage of women with platelet counts that are within 3 standard deviations of the mean? What are the minimum and maximum platelet counts that are within 3 standard deviations of the mean? Data Set 1: Body Data (1000 cells/uL), RED is red blood cell count (million cells/uL), Body and exam measurements are from 300 subjects (first five rows shown here). AGE is in years, for GENDER I = male and 0 = female, PULSE is pulse rate (beats per minute), SYSTOLIC is systolic blood pressure (mm Hg), DIASTOLIC is diastolic blood pressure (mm Hg), HDL is HDL cholesterol (mg/dL), LDL is LDL cholesterol (mg/dL). WHITE is white blood cell count PLATE is platelet count (1000 cells/uL), WEIGHT is weight (kg), HEIGHT is height (cm), WAIST is waist circumference (cm), ARM CIRC is arm circumference (cm), and BMI is body mass index (kg/m2). Data are from the National Center for Health Statistics. TI-83/84 list names AGE, GENDR, PULSE, SYS, DIAS, HDL, (BODY): LDL, WHITE, REDBC, PLATE, WT, HT, WAIST, ARMC, BMI AGE GENDER (1 = M) PULSE SYSTOLIC DIASTOLIC HDL LDL WHITE RED PLATE WEIGHT HEIGHT WAIST ARM CIRC BMI %3D 43 80 100 70 73 68 8.7 4.80 319 98.6 172.0 120.4 40.7 33.3 57 1 84 112 70 35 116 4.9 4.73 187 96.9 186.0 107.8 37.0 28.0 38 94 134 94 36 223 6.9 4.47 297 108.2 154.4 120.3 44.3 45.4 80 1 74 126 64 37 83 7.5 4.32 170 73.1 160.5 97.2 30.3 28.4 34 1 50 114 68 50 104 6.1 4.95 140 83.1 179.0 95.1 34.0 25.9 43. At least 89% of women have platelet counts within 3 standard deviations of the mean. The minimum is 58.9 and the maximum is 451.3.

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Author:Amos Gilat

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