1. BA 275 Quantitative Business Methods
Agenda
Quiz #1
Experiencing Random Behavior
Normal Probability Distribution
Normal Probability Table

2. Review Question: Warranty Level
Mean = 30,000 miles STD = 5,000 miles
Q1: If the level of warranty is set at 15,000 miles, about what % of tires will be returned under the warranty?
Q2: If we can accept that up to 2.5% of tires can be returned under warranty, what should be the warranty level?

3. The Empirical Rule is not Enough
Mean = 30,000 miles STD = 5,000 miles
Q1: If the level of warranty is set at 12,000 miles, about what % of tires will be returned under the warranty?
Q2: If we can accept that up to 3% of tires can be returned under warranty, what should be the warranty level?

4. The Normal Probability Distribution
A specific curve that is symmetric and bell-shaped with two parameters m and s2.
It has been used to describe variables that are too cumbersome to be consider as discrete (i.e., continuous variable). For example,
Physical measurements of members of a biological population (e.g., heights and weights), IQ and exam scores, amounts of rainfall, scientific measurements, etc.
It can be used to describe the outcome of a binomial experiment when the number of trials is large.
It is the foundation of classical statistics.
Central Limit Theorem

5. Standard Normal Probabilities (Table A)

6. Standard Normal Probabilities (Table A)

7. Example 1

8. Example 2

9. Example 3

10. Sampling Distribution (Section 4.4)
A sampling distribution describes the distribution of all possible values of a statistic over all possible random samples of a specific size that can be taken from a population.

11. Central Limit Theorem (CLT)
The CLT applied to Means
With a sample of size n = 25, can we predict the value of
the sample mean?
CLT demo
Example 1: X ~ a normal distribution with the mean 16, and variance 25.
Example 2: X ~ a distribution with the mean 8.08, and variance

12. Answer: Review Question: Warranty Level
Mean = 30,000 miles STD = 5,000 miles
Q1: If the level of warranty is set at 15,000 miles, about what % of tires will be returned under the warranty? => 0.15%
Q2: If we can accept that up to 2.5% of tires can be returned under warranty, what should be the warranty level? => 20,000 miles

13. Answer: The Empirical Rule is not Enough
Mean = 30,000 miles STD = 5,000 miles
Q1: If the level of warranty is set at 12,000 miles, about what % of tires will be returned under the warranty? => almost
Q2: If we can accept that up to 3% of tires can be returned under warranty, what should be the warranty level? => 20,600 miles

14. Answer: Example 1
Prob = 0.025

15. Answer: Example 2
a = -1.41

16. Answer: Example 3
b = 3.14