1 BA 275 Quantitative Business Methods Experiencing Random Behavior Binomial Experiment Binomial Probability Distribution Normal Probability Distribution Quiz #3 Agenda

2 Midterm Exam #1 Wednesday, 2/01/06 in class. Closed books/notes/packet/friends exam, but I will provide you The empirical rule The binomial formula The normal table Need a good night sleep and a calculator that WORKS! Topics: Describing Categorical/Numerical Data The Empirical Rule and Box plot Binomial Distribution The Normal Distribution and the Central Limit Theorem CyberStats: A-1, A-4, A-5, A-6, A-9, B-7, B-9, B-11, B-12.

3 Example Ialpha, a manufacturer of disk drives, buys power switches from a vendor. Ialpha wishes to have fewer than 5% defective switches. To determine whether to accept or reject a shipment, the company decides to inspect 20 power switches and reject the shipment if more than one is defective. Suppose that, in fact, 11% of the switches are defective. What is the chance that Ialpha will accept the shipment?

4 High Speed Internet Connection Claim 1: % of college students who have high speed internet connection is 75% Claim 2: % of college students who have high speed internet connection is 30% A random sample of 12 students was selected to test the claims. SG+ Demo

5 Binomial Distribution A flight is counted as "on time" if it arrived at the gate no more than 15 minutes after the scheduled arrival time. (Bureau of Transportation Statistics) “United Airlines Beats Four Single-Day On-Time Records as Superb Operating Performance Continues” (Press release on 3/2003) Arrival performance “within 14” (early, on time or within 14 minutes of scheduled arrival) at 96.4 percent. Q1. If its performance continues, how likely will you observe 2 late arrivals in the next 5 flights? Q2. If 2 late arrivals are observed in the next 5 flights, do you believe that UA still operates at the record performance?

6 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?

7 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?

8 The Normal Probability Distribution A specific curve that is symmetric and bell-shaped with two parameters  and  2. parameters  and  2 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

9 Notation (p.10) X ~ N( ,  2 ) P( X < a ) = P( X ≤ a ) P( X > b ) = P( X ≥ b ) P( a < X < b ) = P( a ≤ X < b ) = P( a < X ≤ b ) = P( a ≤ X ≤ b )

10 Normal Curve Table (p.40) © 2003 Brooks/Cole Publishing / Thomson Learning™

11 Example 1 (p.11)

12 Example 2 (p.11)

13 Example 3 (p.11)

14 Example 4 (p.11)

15 Example 5 (p.11)

16 Example 6 (p.11)