2. 11.10 NORMAL DISTRIBUTIONS SWBAT: USE A NORMAL DISTRIBUTION, IDENTIFY LEFT AND RIGHT SKEWS, AND APPLY STANDARD DEVIATIONS TO INTERPRET DATA FROM NORMAL DISTRIBUTIONS.

3. DISCRETE VS. CONTINUOUS DISCRETE DATA is counted There are a finite number of possible events The number of students you have in your class The results of rolling 2 dice The number of questions on a test CONTINUOUS DATA is measured Can be any value in an interval of real numbers A person's height: could be any value (within the range of human heights), not just certain fixed heights Time in a race: you could even measure it to fractions of a second A dog's weight

4. There are many cases where the data tends to be around a central value, this creates the NORMAL DISTRIBUTION THE NORMAL DISRIBUTION Data can be “distributed” (spread out) in different ways.

5. A NORMAL DISTRIBUTION Many things follow a normal distribution… Heights of people Size of things produced by machines Errors in measurement Blood pressure Marks on a test

6. REMEMBE R… We can break these Percentages down more

8. SKEWS… Sometimes data are not normal distributed. When a data is being pulled more in one direction or another this is called a SKEW. This means the data does not vary predictably from the mean, therefore we cannot use the percentages from a normal distribution to interpret this data.

9. ANALYZING NORMALLY DISTRIBUTED DATA – EXAMPLE 1 EX 1.2 Approximately what percent of female brown bears in Ex. 1 weigh less than 120 kg? EX 1.3 If the standard deviation is 10, what percent of bears have weights within 1.5 standard deviations of the mean?

10. EXAMPLE 2

11. EXAMPLE 3 The heights of adult American males are approximately normally distributed with mean 69.5 in. and standard deviation 2.5 in. A. What percent of adult American males are between 67 in. and 74.5 in. tall? B. In a group of 2000 adult American males, about how many would you expect to be taller than 6ft (or 72 in.)?