Week 3 Day 2 Standard normal distributions

# Week 3 Day 2 Standard normal distributions

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## Week 3 Day 2 Standard normal distributions

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1. Week 3 Day 2 Standard normal distributions Created by: Tonya Jagoe

2. ALWAYS sketch curve first! Z-Values A set of 500 pieces of data is normally distributed, with a mean of 230 and a standard deviation of 15. Find the z-value associated with the specified x-value by using the formula above, to the nearest hundredth. Then determine what % of the data falls below the specified x-value by using the z-table. x = 240 x = 200 x = 195 x = 260 x = 185

3. ALWAYS sketch curve first! Z-Values A set of 500 pieces of data is normally distributed, with a mean of 230 and a standard deviation of 15. Find the z-value associated with the specified x-value by using the formula above, to the nearest hundredth. Then determine what % of the data falls below the specified x-value by using the z-table. 74.86% x = 240 x = 200 x = 195 x = 260 x = 185 2.28% 0.99% 97.72% 0.13%

4. ALWAYS sketch curve first! Z-Values A set of 500 pieces of data is normally distributed, with a mean of 230 and a standard deviation of 15. Find the z-value associated with the specified x-value by using the formula above. Then determine what % of the data falls above the specified x-value by using the z-table to find the % below and then subtracting from 1. x = 255 x = 210 x = 205 x = 240 x = 180

5. ALWAYS sketch curve first! Z-Values A set of 500 pieces of data is normally distributed, with a mean of 230 and a standard deviation of 15. Find the z-value associated with the specified x-value by using the formula above. Then determine what % of the data falls above the specified x-value by using the z-table to find the % below and then subtracting from 1. 1-0.9525 = 4.75% x = 255 x = 210 x = 205 x = 240 x = 180 1- 0.0918 = 90.82% 1 – 0.0475 = 95.25% 1 – 0.7486 = 25.14% 1 – 0.0004 = 99.96%

6. ALWAYS sketch curve first! Z-Values A set of 500 pieces of data is normally distributed, with a mean of 230 and a standard deviation of 15. Find the z-value associated with the specified x-value by using the formula above. Then determine what % of the data falls between the specified x-values by using the z-table to find the % below each and then subtracting lower from higher. x = 240 to 255 x = 200 to 210 x = 195 to 205 x = 240 to 260 x = 180 to 185

7. ALWAYS sketch curve first! Z-Values A set of 500 pieces of data is normally distributed, with a mean of 230 and a standard deviation of 15. Find the z-value associated with the specified x-value by using the formula above. Then determine what % of the data falls between the specified x-values by using the z-table to find the % below each and then subtracting lower from higher. x = 240 to 255 x = 200 to 210 x = 195 to 205 x = 240 to 260 x = 180 to 185 .9525 - .7486 = 20.39% .0918 - .0228 = 6.9% .04750 - .0099 = 3.76% .9772 - .7486 = 22.86% .0013 - .0004 = 0.09%