How many movies do you watch?

2. How many movies do you watch?

4. Does the CLT apply to means? • The Central Limit Theorem states that the more samples you take, the more Normal your graph will appear for either the sample mean or sample proportion. • What do we need to verify in order to say the distribution should be approximately normal? • Independence Assumption: • In order to be able to consider each sample an unbiased estimator, we must insure that random selection was used. • If we want to insure we aren’t affecting the probability of selecting each sample, we must insure that the sample we take is less then 10% of our population.

5. Does the CLT apply to means?

6. Back to the show…

7. Back to the show… • Suppose that the number of movies viewed in the last year by all high school students in CA has an average of 19.3 and a standard deviation of 15.8 . If we were to randomly sample 100 high school students many times, what would we expect the average of the sampling distribution to be? What about the standard deviation? • Independence Assumption: • We are given that the selection would be random. We can also safely assume that there are more then 1,000 high school students in CA. • Large Enough Condition: • Since n = 100 > 30 we can state that the distribution would be approximately Normal.

8. Example: Awe…Nuts! • At the P. Nutty Peanut Co., dry-roasted, shelled peanuts are placed in jars by a machine. The distribution of the weights in the jars is approximately Normal with a mean of 16.1 oz and a standard deviation of .15 oz. • Without doing any calculations, explain which outcome is more likely: randomly selecting a single jar and finding that it weighs less than 16 oz. or randomly selecting 10 jars and finding that the average is less than 16 oz.? • Find the probability of each of these events.

9. Example: Awe…Nuts! • At the P. Nutty Peanut Co., dry-roasted, shelled peanuts are placed in jars by a machine. The distribution of the weights in the jars is approximately Normal with a mean of 16.1 oz and a standard deviation of .15 oz. • Without doing any calculations, explain which outcome is more likely: randomly selecting a single jar and finding that it weighs less than 16 oz. or randomly selecting 10 jars and finding that the average is less than 16 oz.? • Follow the 4 Step Process! • 1. State what you want to know: • We want to find the probability of selecting a single jar that weighs less then 16 oz.

10. Example: Awe…Nuts! • At the P. Nutty Peanut Co., dry-roasted, shelled peanuts are placed in jars by a machine. The distribution of the weights in the jars is approximately Normal with a mean of 16.1 oz and a standard deviation of .15 oz. • Without doing any calculations, explain which outcome is more likely: randomly selecting a single jar and finding that it weighs less than 16 oz. or randomly selecting 10 jars and finding that the average is less than 16 oz.? • Step 2: Verify Your Assumptions • Independence Assumption: • We are told that the jar is randomly selected. And we can assume that on any given day the P. Nutty Company makes more then 10 jars of peanuts.

11. Example: Awe…Nuts! • At the P. Nutty Peanut Co., dry-roasted, shelled peanuts are placed in jars by a machine. The distribution of the weights in the jars is approximately Normal with a mean of 16.1 oz and a standard deviation of .15 oz. • Without doing any calculations, explain which outcome is more likely: randomly selecting a single jar and finding that it weighs less than 16 oz. or randomly selecting 10 jars and finding that the average is less than 16 oz.? • Step 2: Verify Your Assumptions • Large Enough Condition: • Since we are given that the distribution of weights is approximately Normal, even though our sample is small, it is safe to proceed.

12. Example: Awe…Nuts!

13. Example: Awe…Nuts! This makes sense, because if the distribution is approximately Normal. Then the mean would divide the distribution in half.

14. Example: Awe…Nuts! • At the P. Nutty Peanut Co., dry-roasted, shelled peanuts are placed in jars by a machine. The distribution of the weights in the jars is approximately Normal with a mean of 16.1 oz and a standard deviation of .15 oz. • Without doing any calculations, explain which outcome is more likely: randomly selecting a single jar and finding that it weighs less than 16 oz. or randomly selecting 10 jars and finding that the average is less than 16 oz.? • In your notes, follow the 4 step process to solve this problem. I will randomly select students to come up to the board and show their work.