Chapter 12 – Probability and Statistics 12.7 – The Normal Distribution

Today we will learn how to: Determine whether a set of data appears to be normally distributed or skewed Solve problems involving normally distributed data

12.7 – The Normal Distribution Discrete Probability Distributions – finite number of possible values Histogram Continuous Probability Distribution – outcome can be any value in an interval of real numbers Represented by curves Symmetric Bell curve Normal Distribution

12.7 – The Normal Distribution Skewed Distribution – curve of histogram that is not symmetric Positively skewed – high at the left and tails to the right Negatively skewed – high at the right and tails to the left

12.7 – The Normal Distribution Example 1 Determine whether the data {31, 37, 35, 36, 34, 36, 32, 36, 33, 32, 34, 34, 35, 34} appear to be positively skewed, negatively skewed, or normally distributed

12.7 – The Normal Distribution Using Normal Distributions Standardized test scores, lengths of newborn babies, useful life and size of manufactured items, production levels The number of data values must be large for the distribution to be approximately normal

12.7 – The Normal Distribution Normal Distribution The graph is maximized at the mean The mean, median and mode are about equal About 68% of the values are within one standard deviation of the mean About 95% of the value are within two standard deviations of the mean About 99% of the values are within three standard deviations of the mean

12.7 – The Normal Distribution Example 2 Students counted the number of candies in 100 small packages. They found that the number of candies per package was normally distributed, with a mean of 23 candies per package and a standard deviation of 1 piece of candy. About how many packages had between 22 and 24 candies? What is the probability that a package selected at random had more than 25 candies?

12.6 – Statistical Measures HOMEWORK Page 727 #9 – 19 all