- 4.5.1: Find the area under the normal curve a. To the right of z = 0.85. b...
- 4.5.2: Find the area under the normal curve a. To the left of z = 0.56. b....
- 4.5.3: Let Z N(0, 1). Find a constant c for which a. P(Z c) = 0.1587 b. P(...
- 4.5.4: If X N(2, 9), compute a. P(X 2) b. P(1 X < 7) c. P(2.5 X < 1) d. P(...
- 4.5.5: The lifetime of a battery in a certain application is normally dist...
- 4.5.6: The temperature recorded by a certain thermometer when placed in bo...
- 4.5.7: Scores on a standardized test are approximately normally distribute...
- 4.5.8: Weights of female cats of a certain breed are normally distributed ...
- 4.5.9: The lifetime of a lightbulb in a certain application is normally di...
- 4.5.10: In a certain university, math SAT scores for the entering freshman ...
- 4.5.11: Penicillin is produced by the Penicillium fungus, which is grown in...
- 4.5.12: Specifications for an aircraft bolt require that the ultimate tensi...
- 4.5.13: A cylindrical hole is drilled in a block, and a cylindrical piston ...
- 4.5.14: Shafts manufactured for use in optical storage devices have diamete...
- 4.5.15: The fill volume of cans filled by a certain machine is normally dis...
- 4.5.16: The amount of paint required to paint a surface with an area of 50 ...
- 4.5.17: A fiber-spinning process currently produces a fiber whose strength ...
- 4.5.18: The area covered by 1 L of a certain stain is normally distributed ...
- 4.5.19: Let X N(, 2 ), and let Z = (X )/. Use Equation (4.25) to show that ...
- 4.5.20: The quality-assurance program for a certain adhesive formulation pr...
- 4.5.21: Two resistors, with resistances R1 and R2, are connected in series....
- 4.5.22: The molarity of a solute in solution is defined to be the number of...
- 4.5.23: A binary message m, where m is equal either to 0 or to 1, is sent o...
- 4.5.24: Refer to Exercise 23. Assume that if m = 0, the value s = 1.5 is se...
- 4.5.25: A company receives a large shipment of bolts. The bolts will be use...
- 4.5.26: Chebyshevs inequality (Section 2.4) states that for any random vari...
Solutions for Chapter 4.5: The Normal Distribution
Full solutions for Statistics for Engineers and Scientists | 4th Edition
A method of variable selection in regression that begins with all of the candidate regressor variables in the model and eliminates the insigniicant regressors one at a time until only signiicant regressors remain
An estimator for a parameter obtained from a Bayesian method that uses a prior distribution for the parameter along with the conditional distribution of the data given the parameter to obtain the posterior distribution of the parameter. The estimator is obtained from the posterior distribution.
A distribution with two modes
A chart used to organize the various potential causes of a problem. Also called a ishbone diagram.
Central composite design (CCD)
A second-order response surface design in k variables consisting of a two-level factorial, 2k axial runs, and one or more center points. The two-level factorial portion of a CCD can be a fractional factorial design when k is large. The CCD is the most widely used design for itting a second-order model.
Chi-square (or chi-squared) random variable
A continuous random variable that results from the sum of squares of independent standard normal random variables. It is a special case of a gamma random variable.
Conditional probability mass function
The probability mass function of the conditional probability distribution of a discrete random variable.
When a factorial experiment is run in blocks and the blocks are too small to contain a complete replicate of the experiment, one can run a fraction of the replicate in each block, but this results in losing information on some effects. These effects are linked with or confounded with the blocks. In general, when two factors are varied such that their individual effects cannot be determined separately, their effects are said to be confounded.
Defects-per-unit control chart
See U chart
The response variable in regression or a designed experiment.
Discrete uniform random variable
A discrete random variable with a inite range and constant probability mass function.
A concept in parameter estimation that uses the variances of different estimators; essentially, an estimator is more eficient than another estimator if it has smaller variance. When estimators are biased, the concept requires modiication.
A study in which a sample from a population is used to make inference to the population. See Analytic study
Error mean square
The error sum of squares divided by its number of degrees of freedom.
A subset of a sample space.
Extra sum of squares method
A method used in regression analysis to conduct a hypothesis test for the additional contribution of one or more variables to a model.
Any test of signiicance involving the F distribution. The most common F-tests are (1) testing hypotheses about the variances or standard deviations of two independent normal distributions, (2) testing hypotheses about treatment means or variance components in the analysis of variance, and (3) testing signiicance of regression or tests on subsets of parameters in a regression model.
Fisher’s least signiicant difference (LSD) method
A series of pair-wise hypothesis tests of treatment means in an experiment to determine which means differ.
Fraction defective control chart
See P chart
Gamma random variable
A random variable that generalizes an Erlang random variable to noninteger values of the parameter r