Math1530Homework2.docx - Morgan Terry HOMEWORK 2 1 Normal...

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1 Morgan Terry HOMEWORK 2 1 Normal Distributions 1.1 Using the 68-95-99.7 Rule Scores on a University exam are normally distributed with a mean µ of 68 and a standard deviation σ of 9. Use the 68-95-99.7 Rule to answer the following questions. 1. Draw the Density Curve and label ± 3 σ away from the mean. 100 90 80 70 60 50 40 0.05 0.04 0.03 0.02 0.01 0.00 X Density Distribution Plot Normal, Mean=68, StDev=9 2. What proportion of students score between a 59 to 77? 68% 3. What proportion of students score between a 50 to 86? 95% 4. What proportion of students score above a 86? 2.5% 5. What proportion of students score below a 41? 0.15% 6. What proportion of students score above a 59? 83.85% 7. What must a student score on the exam to be in the bottom 2.5% of scores on the exam? 50%
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2 Morgan Terry 1.2 Using Table A (Standard Normal Distribution) to find Percentiles 1. Find z < 1 . 96 97.50% 2. Find z < 2 . 46 0.69% 3. Find z < 0 . 43 33.36% 4. Find z > 2 . 13 1.66% 5. Find z > 1 . 50 6.68% 6. Find z > − 1 . 00 84.13% 7. Find 1 . 25 < z < 1 . 75 85.43% 8. Find 0 . 63 < z < 2 . 01 24.21% a. Finding Proportions for a Normal Distribution with mean µ and standard deviation σ (AKA Finding z- scores to use Table A) It has been shown that lengths of pregnancies follow a Normal Distribution with mean µ of 266 days and standard deviation σ of 16 days. Use this information to answer the following questions. i. Draw the Density Curve for Lengths of Pregnancies.
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3 Morgan Terry 320 300 280 260 240 220 0.025 0.020 0.015 0.010 0.005 0.000 X Density Distribution Plot Normal, Mean=266, StDev=16 ii. What proportion of pregnancies last less than 275 days? 71.31% iii. What proportion of pregnancies last more than 275 days?
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