1. Thinking Mathematically Statistics: 12.5 Problem Solving with the Normal Distribution

2. Percentiles If n% of the items in a distribution are less than a particular data item, we say that the data item is in the nth percentile of the distribution. For example, if a student scored in the 93rd percentile on the SAT, the student did better than about 93% of all those who took the exam.

3. Percentiles and z-scores Table 12.14 in the text relates z-scores to percentiles. To determine the percent below a value, compute the z- score and look-up the corresponding percentile in table 12.14 To determine the percent above, compute z-score, look-up percentile, and subtract from 100 To determine the percent between two values, compute both z-scores, look-up percentiles, and subtract.  What % falls between z values of -1, +1? -2, +2? -3, +3?

4. - 3 - 2 - 1 231 68% 95% 99.7% The 68-95-99.7 Rule for the Normal Distribution

5. Examples: Percentiles Exercise Set 12.5 #7, 11 Find the percentage of data items in a normal distribution that a)Lie below a z score of -1.2 b)Lie above a z score of -1.2 Find the percentage of data items in a normal distribution that lie between z = 1 and z = 3.

6. Examples: Percentiles Exercise Set 12.5 #19, 25 Systolic blood pressure readings are normally distributed with a mean of 121 and a standard deviation of 15. Find the percentage of readings above 130. Find the percentage of readings between 112 and 130.

7. Thinking Mathematically Statistics: 12.4 The Normal Distribution