1. 8-5 day 2 Applications from statistics

2. NORMAL PROBABILITIES
Probability Density Function (pdf) is a function f (x), where the domain is all real numbers, such that f (x)  0 for all x
and
The probability associated with an interval [a, b] is
Ex 5) Find the probability that an old clock you found stopped between 2:00 and 5:00.
pdf of clock:

3. NORMAL CURVE
We need:
Normal pdf (Gaussian Curve)
For a population with mean  and standard deviation , the normal probability density function is

4. 68% of area lies within  of  95% of area lies within 2 of 
Rule
Given a normal curve:
68% of area lies within  of 
95% of area lies within 2 of 
99.7% of area lies within 3 of 
*Depending on the value of , the curve could be tall/skinny or short/fat

5. Ex 6) Suppose a telephone help line takes a mean of 2 minutes to answer calls. If the standard deviation is  = 0.5, then:
________ % of the calls are answered in the range of to 2.5 minutes, and
________ % of the calls are answered in the range of to 3.5 minutes 68
99.7

6. Ex 7) Suppose that frozen spinach boxes marked as “10 ounces” of spinach have a mean weight of 10.3 ounces and a standard deviation of 0.2 ounces. Assume that the weights of the spinach boxes are normally distributed.
Formula:
Quick Graph Sketch:
a) What percentage of all such spinach boxes can be expected to weigh between 10 and 11 ounces?
fnInt

7. b) What percentage would we expect to weigh less than 10 ounces?  
c) What is the probability that a box weighs exactly 10 ounces?

8. homework
Pg. 429 # 3, 7, 10, 26, 30, 31, 38, 39