“Life shrinks or expands in proportion to one’s courage .” – Anais Nin

1. “Life shrinks or expands in proportion to one’s courage.” –Anais Nin

2. P.O.D. #3 basic advanced A bag contains 150 marbles. The probability that you will pick a blue marble from the bag is 7/10. How many blue marbles are in the bag? 7 19 x 57 = 7 57 = 19  x 399 = 19x ÷19 ÷19 21 = x 7 10 x 150 = 7150 = 10  x 1,050 = 10x ÷10 ÷10 105 = x

3. Using a Sample to Make Predictions

4. A population is an entire group of items or individuals. A sample is part of a population that is selected for the purpose of collecting data about that population. Example: You want to know the number of students in your classroom who do their homework right after school. You survey the first 10 students who arrive in the classroom. Population – All students in the class Sample – The first 10 students who arrive

5. An unbiased sample is representative of a population. It is selected at random and is large enough to provide accurate data. A biased sample is not representative of a population. One or more parts of the population are favored over others. A biased sample may lead to incorrect conclusions.

6. Example: You want to estimate the number of students in a high school who ride the school bus. Which sample is unbiased? a) 4 students in the hallway b) All students in the marching band d) 100 students at random during lunch c) 50 seniors at random

7. You can use data collected about a sample to make predictions about the entire population.

8. Example: You ask 75 randomly chosen students how many movies they watch each week. There are 1200 students in the school. Predict the number of students in the school who watch one movie each week. 21 75 x 1200 = Set up a proportion: Cross multiply: 21  1200 = 75  x 25,200 = 75x ÷75 ÷75 336 = x Solve for variable: I predict that 336 students watch one movie each week.

9. Whiteboard: A scientist studies lions on a wildlife preserve to learn about the parenting habits of lions. Identify the population and the sample. Population - All Lions Sample - Lions on the Preserve

10. Whiteboard: You want to predict the number of residents in Philadelphia who own a home. Which sample is better for making a prediction.

11. Whiteboard: To find how much money the average American family spends to cool their home, 100 Alaskan families are surveyed at random. Is this sample unbiased or biased? This sample is biased.

12. Whiteboard: In a survey, 200 people from a town were asked if they thought the town needed more bicycle paths. 39% of those surveyed said the town needs more bicycle paths. Predict how many of the 8,000 people in the town think more bicycle paths are needed. 39 100 x 8000 = 39  8000 = 100  x 312,000 = 100x ÷100 ÷100 3,120 = x