ETS/Theodore Tutorials Probability and Statistics A Self-Instructional Problem Workbook Francis B. Taylor Department of Mathematics and Computer Science Manhattan College, Riverdale NY Published by ETS Professional Training Institute © 1994 Louis Theodore. 186 pages. ISBN 1-882767-13-6. Table of Contents Basic Operations Calculating the Probability of An Event · Application of the Addition Theorem · Application of the Multiplication Theorem · Calculation of Expected Value: Discrete Case · Calculation of Expected Value: Continuous Case · Calculation and Interpretation of Mean and Variance: Discrete Case · Calculation and Interpretation of Mean and Variance: Continuous Case · Probability Calculations for Standard Normal Variables · Probability Calculations for Non-Standard Normal Variables · Estimation of Population Mean and Variance · Probability Calculations Concerning the Sample Mean · Calculation of Type I and Type II Errors in Testing Hypotheses Problems Bayes' Theorem (BAY) BAY. 1: Plant Origins of Defective Items BAY. 2: Cause of Chemical Plant Explosion Reliability (REL) REL. 1: Reliability of Series and Parallel Systems REL. 2: Reliability of Overseas Flight Binomial Distribution (BIN) BIN. 1: Sampling With Replacement BIN. 2: Sampling Without Replacement Hypergeometric Distribution (HYP) HYP. 1: Sampling Without Replacement HYP. 2: Acceptance Sampling Plan Evaluation Poisson Distribution (POI) POI. 1: Computer Breakdowns POI. 2: Defective Welds POI. 3: Reliability of Standby Redundant System Weibull Distribution (WEI) WEI. 1: Failure Probability from Failure Rate Using the Weibull Distribution WEI. 2: Estimation of Weibull Parameters Log-Normal Distribution (LNO) LNO. 1: Time to Failure of Electric Motors LNO. 2: Interrequest Times for Computer Service Monte Carlo Simulation (MCS) MCS. 1: Monte Carlo Simulation of Time to Failure MCS. 2: Monte Carlo Simulation of Normally Distributed Times to Failure Confidence Intervals for Means (CIM) CIM. 1: Large Sample Confidence Interval for Urban Population Mean Ozone Measurement CIM. 2: Small Sample Confidence Interval for Population Mean Gas Mileage Confidence Intervals for Proportions (CIP) CIP. 1: Large Sample Confidence Interval for Proportion of Accidents Due to Unsafe Working Conditions CIP. 2: Sample Size for Estimating Proportion Defective Testing Hypotheses Concerning Means (THM) THM. 1: Large Sample Test of Hypothesis Concerning Mean Compressive Strength of Steel Beams THM. 2: Small Sample Test of Hypothesis Concerning Mean Tar Content of Cigarettes Testing Hypotheses Concerning Variances (THV) THV. 1: Testing Hypothesis Concerning the Variability of Gas Mileage THV. 2: Comparison of the Variability of Battery Life for Two Brands of Battery Chi-Square Tests (CHI) CHI. 1: Testing Assumption Concerning Pdf of Interrequest Times for Computer Service CHI. 2: Independence of Work Shift and Quality of Output Regression Analysis (REG) REG. 1: Linear Regression of Yield of Chemical Reaction on Temperature REG. 2: Correlation of Resistance and Failure Time of Transistors Analysis of Variance (ANV) ANV. 1: Comparison of Effect of Food Supplements on Milk Yield ANV. 2: Effect of Rubber Mix and Curing Time on Tensile Strength ANV. 3: Diet and Drug Effects on Stimulus Response Time Nonparametric Tests (NPT) NPT. 1: Paired Comparison of Instruments Measuring Sulfur Dioxide Concentration NPT. 2: Comparison of Disconnect Forces Required to Separate Electrical Connectors Solutions to Problems Table I. Areas under a standard normal curve Table II. Student's Distribution Table III. Chi-Square Distribution Table IV. F-Distribution (A) Table V. F-Distribution (B) Copyright © 1999, ETS Incorporated