week 3 day 2 standard normal distributions
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Week 3 Day 2 Standard normal distributions. Created by: Tonya Jagoe. ALWAYS sketch curve first!. Z-Values. - PowerPoint PPT PresentationTRANSCRIPT
1Created by: Tonya Jagoe
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
z ALWAYS sketch curve first!
1. x = 240
2. x = 200
3. x = 195
4. x = 260
5. x = 185
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.
1. x = 240
2. x = 200
3. x = 195
4. x = 260
5. x = 185
x
z ALWAYS sketch curve first!
67.015
230240
z
00.215
230200
z
33.215
230195
z
00.215
230260
z
00.315
230185
z
74.86%
2.28%
0.99%
97.72%
0.13%
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
z ALWAYS sketch curve first!
1. x = 255
2. x = 210
3. x = 205
4. x = 240
5. x = 180
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
z
1. x = 255
2. x = 210
3. x = 205
4. x = 240
5. x = 180
ALWAYS sketch curve first!
67.115
230255
z
33.115
230210
z
67.115
230205
z
67.015
230240
z
33.315
230180
z
1-0.9525 = 4.75%
1- 0.0918 = 90.82%
1 – 0.0475 = 95.25%
1 – 0.7486 = 25.14%
1 – 0.0004 = 99.96%
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
z ALWAYS sketch curve first!
1. x = 240 to 255
2. x = 200 to 210
3. x = 195 to 205
4. x = 240 to 260
5. x = 180 to 185
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
z
1. x = 240 to 255
2. x = 200 to 210
3. x = 195 to 205
4. x = 240 to 260
5. x = 180 to 185
ALWAYS sketch curve first!
9525.0;255
7486.0;240 .9525 - .7486 = 20.39%
.0918 - .0228 = 6.9%
.04750 - .0099 = 3.76%
.9772 - .7486 = 22.86%
.0013 - .0004 = 0.09%
0934.0;210
0228.0;200
0475.0;205
0099.0.0;195
9772.0;260
7486.0;240
0013.0;185
0004.0;180