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

“Normal Distribution.” 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.

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

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:

In summary (Empirical Rule): About 99.7% within 3 s.d. of mean 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%)

The data for adult IQ scores has a bell-shaped distribution where the mean IQ score of adults is 100, with a standard deviation of 15. Use the Empirical Rule to sketch the distribution and breakdown of percents.

The data for adult IQ scores has a bell-shaped distribution where the mean IQ score of adults is 100, with a standard deviation of 15. Find the percentage of adults with scores between 70 and 130. Find the percentage of adults with IQ scores between 55 and 85. Find the percentage of adults with a score of 130 or higher.   In a sample of 500 adults, approximately how many of them would you expect to have an IQ less than 70?

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, Sketch the distribution and break down of percents.

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, Sketch the distribution and break down of percents. Find the mean for the students’ heights

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, Sketch the distribution and break down of percents. Find the standard deviation for the students’ heights

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, Sketch the distribution and break down of percents. What percent of students can we expect to have heights less than 1.25 m? How many students are shorter than 1.25 m?

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, Sketch the distribution and break down of percents. What percent of students can we expect to be taller than 1.7 m? How many LHS students are taller than 1.7 m?

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, Sketch the distribution and break down of percents. 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?

Memorize! About 99.7% within 3 s.d. of mean