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

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?

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?

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

Standard Normal Probabilities (Table A)

Standard Normal Probabilities (Table A)

Example 1

Example 2

Example 3

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.

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 38.6884.

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

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 0.0000 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

Answer: Example 1 Prob = 0.025

Answer: Example 2 a = -1.41

Answer: Example 3 b = 3.14