SECONDARY MATH 3 9-4 Normal Distribution. Graph the function on the graphing calculator Identify the x and y intercepts Identify the relative minimums.

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SECONDARY MATH Normal Distribution

Graph the function on the graphing calculator Identify the x and y intercepts Identify the relative minimums and maximums Identify where increasing/decreasing Identify where positive/negative Determine end behavior. Determine symmetry

What you will learn The shape of a normal distribution and examples of normally distributed data. How to use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. How to use technology or tables to estimate areas under the normal curve.

Symmetric Distribution Also called: NORMAL DISTRIBUTION BELL-CURVE If you drew a line through the center, then each half is a mirror image of the other.

Number of Peaks

Skewed Data Skewed Left  Most of the data is on the right side, but there is a “tail” on the left side. Skewed Right  Most of the data is on the left side, but there is a “tail” on the right side.

UNIFORM The data points are equally spread across the range, with NO clear peaks.

Describe the distribution of the following: What would be the best measure of central tendency to use? Why?

This is the data on the number of goals scored by the 2004 U.S. women’s soccer team in 34 games played during the 2004 seasons Determine the following: Median: Mean: Mode: Standard Deviation: Create a histogram and describe the distribution.

The area under a normal curve is always 1. When calculating population percentages, the value will be less than 1.

ACT test scores are approximately normally distributed. One year the scores had a mean of 21 and a standard deviation of 5.2.

c. What percentage of ACT scores is between 28 and 36? What would you estimate the percentage would be? Use the calculator – normalcdf(28, 36, 21, 5.2) 8.7%

2000 freshmen at Weber State University took a biology test. The scores were distributed normally with a mean of 70 and a standard deviation of 5. Label the mean and three standard deviations from the mean. 1.What percentage of scores are between 65 and 75? 2.What percentage of scores are between 60 and 70? 3.What percentage of scores are between 60 and 85? 4.What percentage of scores is less than a score of 55? 5.What percentage of scores is greater than a score of 80?

The mathematics portion of the SAT has a mean score of 500 and a standard deviation of 100. (800 is the highest score you can get).

The mathematics portion of the SAT has a mean score of 500 and a standard deviation of 100. C. What percentage of SAT scores is between 325 and 615? = 83.5% normalcdf(325,615,500,100)