Understanding Normal Probability Distribution and Warranty Levels in Business
This quiz explores the application of normal probability distribution in analyzing warranty levels for tires. It focuses on calculating the percentage of tires that will be returned under specific warranty conditions and determining optimal warranty levels based on acceptable return rates. Topics covered include the Empirical Rule, Central Limit Theorem, and sampling distribution, providing a comprehensive understanding of statistical methods in business contexts. The agenda incorporates questions on real-world scenarios to enhance quantitative analysis skills.
Understanding Normal Probability Distribution and Warranty Levels in Business
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Presentation Transcript
BA 275Quantitative Business Methods • Quiz #1 • Experiencing Random Behavior • Normal Probability Distribution • Normal Probability Table Agenda
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
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
