1. Created by: Tonya Jagoe

2. Notice The mean is always pulled the farthest into the tail. The median is always in the middle – located between the mean and the mode. The mode is always at the highest point – the data that is MOST represented.

3. For each grouping, identify as Normal, Positively Skewed, or Negatively Skewed. Then, mark on each drawing the approximate locations of the mean, median, and mode.

4. NORMAL DISTRIBUTIONS Empirical Rule (68 – 95 – 99.7 Rule) 68% within 1 standard deviation 34% 99.7% within 3 standard deviations 2.35% 95% within 2 standard deviations 13.5% 4 of 149 © 2012 Pearson Education, Inc. All rights reserved.

5. Sketch as a normal distribution, then use the Empirical Rule to answer the question. Normally distributed data with a mean of 42 and a standard deviation of 4.7. 1.Find the interval of the data that falls within one standard deviation of the mean. What % of the data does this represent? 2.Find the interval of the data that falls within two standard deviations of the mean. What % of the data does this represent? 3.Find the interval of the data that falls within three standard deviations of the mean. What % of the data does this represent? 4.For what values of x would the data fall outside three standard deviations of the mean. What % of the data does this represent? 34% 13.5% 2.35% 42 46.7 51.456.1 37.3 32.6 27.9 x 56.1 0.3% 99.7% 27.9 < x < 56.1 95% 32.6 < x < 51.4 68% 37.3< x < 46.7

6. Sketch as a normal distribution, then use the Empirical Rule to answer the question. Normally distributed data with a mean of 112 and a standard deviation of 19.3. 1.Find the interval of the data that falls within one standard deviation of the mean. What % of the data does this represent? 2.Find the interval of the data that falls within two standard deviations of the mean. What % of the data does this represent? 3.Find the interval of the data that falls within three standard deviations of the mean. What % of the data does this represent? 4.For what values of x would the data fall outside two standard deviations of the mean. What % of the data does this represent? 34% 13.5% 2.35% 112 131.3 150.6169.9 92.7 73.4 54.1 x 150.6 5% 99.7% 54.1 < x < 169.9 95% 73.4 < x < 150.6 68% 92.7 < x < 131.3