1. Ch.18 Normal approximation using probability histograms Review measures of center and spread For a “large” number of draws, a histogram of observed sums is like a normal curve. CenterSpreadTypical outcome List of #sAverageSDAvg. SD Box modelEV of sumSE of sumEV SE

2. A probability histogram represents chance by area. –The value in the middle of the base of the rectangle represents the sum. –The area of the rectangle equals the chance of getting that particular sum.

3. Example 1: Coin toss 4 times and count the number of heads. 1.Draw a box model 2.List the possible outcomes 3.Draw a probability histogram 4.What is the probability of getting exactly 2 heads? 5.What is the probability of getting 2 or fewer heads?

4. Activity Probability Histogram Empirical Histogram

5. If the total number of repetitions is large, the histogram for the observed sums (data) is approximately the probability histogram (theory). (Law of averages) If the number of draws is large (drawing with replacement), the probability histogram for the sum of the draws is approximately the normal curve. (Central limit theorem)

6. Example 2: What is the chance of getting exactly 50 heads in 100 coin tosses? Example 3: Using the setting from the probability histogram activity, what is the chance of getting a sum of 3 in 2 draws? What is the chance of getting a sum less than or equal to 3 in 2 draws?