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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)
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