Transcript Warm-up

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?
Continuous Random
Variables
Density Functions
Continuous Random Variables

Possible values contain an entire interval.
Ex: Weight of newborns

Nearest pound
4

5
6
7
8
9
Nearest tenth of pound
4
5
6
7
8
9
Fit more & more rectangles

It approaches a curve as the rectangles
become smaller & has greater accuracy.
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.
•
Uniform Distribution

All occur in equal distributions
Ex:
.5 if 4  x  6
f ( x)  
0 otherwise
What’s the area from 4.5 to 5.5?
What’s the area from 5.5 to 6?
Discrete:
P(3  x  7)  P(3)  P (4)  P(5)  P (6)  P(7)
P(3  x  7)  P(4)  P(5)  P(6)
Continuous:
P(3  x  7)  P(3  x  7)
Why?
It’s like finding the area of a rectangle with width = 0.
Probabilities for continuous random
variables are usually calculated using
cumulative areas.
P(x<0.5)
Found using integrals & calculus – but we’ll use tables!
If we have a uniform continuous
function from 3 to 8, find the height.
Ex.
0.02
50 minutes

Find P(x < 10)

Find P(x < 35)
0.25
Ex:

Find P(x<4)

Find P(x<2)
0.02
Ex:
50

Find P(x<20)

Find P(x>70)

Find P(20<x<70)
100
Homework

P. 365 (20-26)