1. Warm-up 1. A concert hall has 2000 seats. There are 1200 seats on the main floor and 800 in the balcony. 40% of those in the balcony buy a souvenir program. 50% of those on the main floor buy a souvenir program. At a certain performance all seats are occupied. If an audience member is selected at random, what is the probability that a program was purchased? 2. A spinner on a full circle can take on any decimal value between 0 and 400. What is the probability that the spinner will land between 175 and 225?

2. Continuous Random Variables Density Functions

3. Continuous Random Variables Possible values contain an entire interval.

4. Ex: Weight of newborns Nearest pound Nearest tenth of pound 456789 456789

5. Fit more & more rectangles It approaches a curve as the rectangles become smaller & has greater accuracy.

6. Density Function Probability distribution for a continuous random variable (f(x)). The graph is a smooth curve called the density curve. F(x)  0 Total area under the curve = 1.

7. Uniform Distribution All occur in equal distributions

8. Ex: What’s the area from 4.5 to 5.5?What’s the area from 5.5 to 6?

9. Discrete:

10. Continuous: Why? It’s like finding the area of a rectangle with width = 0.

11. Probabilities for continuous random variables are usually calculated using cumulative areas. P(x<0.5) Found using integrals & calculus – but we’ll use tables!

12. If we have a uniform continuous function from 3 to 8, find the height.

13. Ex. Find P(x < 10) Find P(x < 35) 0.02 50 minutes

14. Ex: Find P(x<4) Find P(x<2) 0.25

15. Ex: Find P(x<20) Find P(x>70) Find P(20<x<70) 0.02 50 100

16. Homework P. 365 (20-26)