2. When we collect data from an experiment, it can be “distributed” (spread out) in different ways.

3. There are many cases where the data tends to be around a central value, equally spread left and right, getting close to a “Normal Distribution.” The yellow histogram shows data that follows closely, not necessarily perfectly, a bell curve.

4. The Normal Distribution has: Mean = Median = Mode Symmetry about the center 50% of values smaller than the mean and 50% of values greater than the mean

5. Remember that the Standard Deviation is a measure of how spread out numbers are for a set of data. After you compute the standard deviation for a Normal Distribution, you will find out:

7. In summary (Empirical Rule): 99.7% We can say that in a Normal Distribution any value is: Likely to be within 1 standard deviation of the mean (68%) Very likely to be within 2 standard deviations of the mean (95%) Almost certain to be within 3 standard deviations of the mean (99.7%)

8. Example: At Liberty, 95% of students are between 1.1 m and 1.7 m tall. Assuming this data is normally distributed and there are 1,800 students at LHS, 1)Find the mean for the students’ heights 1.1 1.7

9. Example: At Liberty, 95% of students are between 1.1 m and 1.7 m tall. Assuming this data is normally distributed and there are 1,800 students at LHS, 1)Find the mean for the students’ heights 1.1 1.40 1.7

10. Example: At Liberty, 95% of students are between 1.1 m and 1.7 m tall. Assuming this data is normally distributed and there are 1,800 students at LHS, 1)Find the mean for the students’ heights 2)Find the standard deviation for the students’ heights 1.1 1.40 1.7

11. Example: At Liberty, 95% of students are between 1.1 m and 1.7 m tall. Assuming this data is normally distributed and there are 1,800 students at LHS, 1)Find the mean for the students’ heights 2)Find the standard deviation for the students’ heights 1.1 1.25 1.40 1.55 1.7

12. Example: At Liberty, 95% of students are between 1.1 m and 1.7 m tall. Assuming this data is normally distributed and there are 1,800 students at LHS, 1)Find the mean for the students’ heights 2)Find the standard deviation for the students’ heights 3)What percent of students can we expect to have heights less than 1.25 m? How many LHS students are shorter than 1.25 m? 0.95 1.1 1.25 1.4 1.55 1.7 1.85

13. Example: At Liberty, 95% of students are between 1.1 m and 1.7 m tall. Assuming this data is normally distributed and there are 1,800 students at LHS, 1)Find the mean for the students’ heights 2)Find the standard deviation for the students’ heights 3)What percent of students can we expect to have heights less than 1.25 m? How many LHS students are shorter than 1.25 m? 4)What percent of students can we expect to be taller than 1.7 m? How many LHS students are taller than 1.7 m? 0.95 1.1 1.25 1.4 1.55 1.7 1.85

14. Example: At Liberty, 95% of students are between 1.1 m and 1.7 m tall. Assuming this data is normally distributed and there are 1,800 students at LHS, 1)Find the mean for the students’ heights 2)Find the standard deviation for the students’ heights 3)What percent of students can we expect to have heights less than 1.25 m? How many students are shorter than 1.25 m? 4)What percent of students can we expect to be taller than 1.7 m? How many LHS students are taller than 1.7 m? 5)What percent of students can we expect to have heights between 0.95 m and 1.85 m? How many LHS students have heights between 0.95 m and 1.85 m? 0.95 1.1 1.25 1.4 1.55 1.7 1.85