BA 275 Quantitative Business Methods Agenda n Quiz

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

Review Question: Warranty Level Mean = 30, 000 miles STD = 5, 000 miles Q 1: If the level of warranty is set at 15, 000 miles, about what % of tires will be returned under the warranty? Q 2: If we can accept that up to 2. 5% of tires can be returned under warranty, what should be the warranty level? 2

The Empirical Rule is not Enough Mean = 30, 000 miles STD = 5, 000 miles Q 1: If the level of warranty is set at 12, 000 miles, about what % of tires will be returned under the warranty? Q 2: If we can accept that up to 3% of tires can be returned under warranty, what should be the warranty level? 3

The Normal Probability Distribution n A specific curve that is symmetric and bell-shaped with two parameters m and s 2. n It has been used to describe variables that are too cumbersome to be consider as discrete (i. e. , continuous variable). For example, n Physical measurements of members of a biological population (e. g. , heights and weights), IQ and exam scores, amounts of rainfall, scientific measurements, etc. n It can be used to describe the outcome of a binomial experiment when the number of trials is large. n It is the foundation of classical statistics. n Central Limit Theorem 4

Standard Normal Probabilities (Table A) 5

Standard Normal Probabilities (Table A) 6

Example 1 7

Example 2 8

Example 3 9

Sampling Distribution (Section 4. 4) n 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. 10

Central Limit Theorem (CLT) n The CLT applied to Means CLT demo With a sample of size n = 25, can we predict the value of the sample mean? 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 38. 6884. 11

Answer: Review Question: Warranty Level Mean = 30, 000 miles STD = 5, 000 miles Q 1: If the level of warranty is set at 15, 000 miles, about what % of tires will be returned under the warranty? => 0. 15% Q 2: 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 12

Answer: The Empirical Rule is not Enough Mean = 30, 000 miles STD = 5, 000 miles Q 1: If the level of warranty is set at 12, 000 miles, about what % of tires will be returned under the warranty? => almost 0. 0000 Q 2: If we can accept that up to 3% of tires can be returned under warranty, what should be the warranty level? => 20, 600 miles 13

Answer: Example 1 Prob = 0. 025 14

Answer: Example 2 a = -1. 41 15

Answer: Example 3 b = 3. 14 16