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

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)

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