 6.6.1: Given a continuous uniform distribution, show that (a) = A+B 2 and ...
 6.6.2: Suppose X follows a continuous uniform distribution from 1 to 5. De...
 6.6.3: The daily amount of coee, in liters, dispensed by a machine located...
 6.6.4: A bus arrives every 10 minutes at a bus stop. It is assumed that th...
 6.6.5: Given a standard normal distribution, nd the area under the curve t...
 6.6.6: Find the value of z if the area under a standard normal curve (a) t...
 6.6.7: Given a standard normal distribution, nd the value of k such that (...
 6.6.8: Given a normal distribution with = 30 and = 6, nd (a) the normal cu...
 6.6.9: Given the normally distributed variable X with mean 18 and standard...
 6.6.10: According to Chebyshevs theorem, the probability that any random va...
 6.6.11: A softdrink machine is regulated so that it discharges an average ...
 6.6.12: The loaves of rye bread distributed to local stores by a certain ba...
 6.6.13: A research scientist reports that mice will live an average of 40 m...
 6.6.14: The nished inside diameter of a piston ring is normally distributed...
 6.6.15: A lawyer commutes daily from his suburban home to his midtown oce. ...
 6.6.16: In the November 1990 issue of Chemical Engineering Progress, a stud...
 6.6.17: The average life of a certain type of small motor is 10 years with ...
 6.6.18: The heights of 1000 students are normally distributed with a mean o...
 6.6.19: A company pays its employees an average wage of $15.90 an hour with...
 6.6.20: The weights of a large number of miniature poodles are approximatel...
 6.6.21: The tensile strength of a certain metal component is normally distr...
 6.6.22: If a set of observations is normally distributed, what percent of t...
 6.6.23: The IQs of 600 applicants to a certain college are approximately no...
 6.6.24: A coin is tossed 400 times. Use the normal curve approximation to n...
 6.6.25: A process for manufacturing an electronic component yields items of...
 6.6.26: A process yields 10% defective items. If 100 items are randomly sel...
 6.6.27: The probability that a patient recovers from a delicate heart opera...
 6.28E: Let ?X?1, ?X?2, . . . , ?X?n? ?represent a random sample from the R...
 6.6.28: Researchers at George Washington University and the National Instit...
 6.6.29: If 20% of the residents in a U.S. city prefer a white telephone ove...
 6.6.30: A drug manufacturer claims that a certain drug cures a blood diseas...
 6.6.31: Onesixth of the male freshmen entering a large state school are ou...
 6.6.32: A pharmaceutical company knows that approximately 5% of its birthc...
 6.6.33: Statistics released by the National Highway Trac Safety Administrat...
 6.6.34: A pair of dice is rolled 180 times. What is the probability that a ...
 6.6.35: A company produces component parts for an engine. Parts specication...
 6.6.36: A common practice of airline companies is to sell more tickets for ...
 6.6.37: The serum cholesterol level X in 14yearold boys has approximately...
 6.6.38: A telemarketing company has a special letteropening machine that op...
 6.6.39: Use the gamma function with y = 2x to show that (1/2) =.
 6.6.40: In a certain city, the daily consumption of water (in millions of l...
 6.6.41: If a random variable X has the gamma distribution with = 2 and = 1,...
 6.6.42: Suppose that the time, in hours, required to repair a heat pump is ...
 6.6.43: (a) Find the mean and variance of the daily water consumption in Ex...
 6.6.44: In a certain city, the daily consumption of electric power, in mill...
 6.6.45: The length of time for one individual to be served at a cafeteria i...
 6.6.46: The life, in years, of a certain type of electrical switch has an e...
 6.6.47: Suppose that the service life, in years, of a hearing aid battery i...
 6.6.48: Derive the mean and variance of the beta distribution.
 6.6.49: Suppose the random variable X follows a beta distribution with = 1 ...
 6.6.50: If the proportion of a brand of television set requiring service du...
 6.6.51: The lives of a certain automobile seal have the Weibull distributio...
 6.6.52: Derive the mean and variance of the Weibull distribution.
 6.6.53: In a biomedical research study, it was determined that the survival...
 6.6.54: The lifetime, in weeks, of a certain type of transistor is known to...
 6.6.55: Computer response time is an important application of the gamma and...
 6.6.56: Rate data often follow a lognormal distribution. Average power usag...
 6.6.57: For Exercise 6.56, what is the mean power usage (average dB per hou...
 6.6.58: The number of automobiles that arrive at a certain intersection per...
 6.6.59: Consider the information in Exercise 6.58. (a) What is the probabil...
 6.6.60: Show that the failurerate function is given byZ(t)=t1, t > 0,if an...
 6.6.61: According to a study published by a group of sociologists at the Un...
 6.6.62: The exponential distribution is frequently applied to the waiting t...
 6.6.63: When is a positive integer n, the gamma distribution is also known ...
 6.6.64: A manufacturer of a certain type of large machine wishes to buy riv...
 6.6.65: According to a recent census, almost 65% of all households in the U...
 6.6.66: A certain type of device has an advertised failure rate of 0.01 per...
 6.6.67: In a chemical processing plant, it is important that the yield of a...
 6.6.68: For an electrical component with a failure rate of once every 5 hou...
 6.6.69: The elongation of a steel bar under a particular load has been esta...
 6.6.70: A controlled satellite is known to have an error (distance from tar...
 6.6.71: A technician plans to test a certain type of resin developed in the...
 6.6.72: Consider the information in Review Exercise 6.66. What is the proba...
 6.6.73: For Review Exercise 6.72, what are the mean and variance of the tim...
 6.6.74: The average rate of water usage (thousands of gallons per hour) by ...
 6.6.75: For Review Exercise 6.74, what is the mean of the average water usa...
 6.6.76: In Exercise 6.54 on page 206, the lifetime of a transistor is assum...
 6.6.77: The beta distribution has considerable application in reliability p...
 6.6.78: Consider now Review Exercise 3.74 on page 108. The density function...
 6.6.79: Consider Review Exercise 6.78. Given the assumption of the exponent...
 6.6.80: In a human factor experimental project, it has been determined that...
 6.6.81: The length of time between breakdowns of an essential piece of equi...
 6.6.82: The length of life, in hours, of a drill bit in a mechanical operat...
 6.6.83: The length of life, in hours, of a drill bit in a mechanical operat...
 6.6.84: Explain why the nature of the scenario in Review Exercise 6.82 woul...
 6.6.85: From the relationship between the chisquared random variable and t...
 6.6.86: The length of time, in seconds, that a computer user takes to read ...
 6.6.87: Group Project: Have groups of students observe the number of people...
Solutions for Chapter 6: Some Continuous Probability Distributions
Full solutions for Probability and Statistics for Engineers and the Scientists  9th Edition
ISBN: 9780321629111
Solutions for Chapter 6: Some Continuous Probability Distributions
Get Full SolutionsSummary of Chapter 6: Some Continuous Probability Distributions
One of the simplest continuous distributions in all of statistics is the continuous uniform distribution.
Since 88 problems in chapter 6: Some Continuous Probability Distributions have been answered, more than 447595 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 6: Some Continuous Probability Distributions includes 88 full stepbystep solutions. Probability and Statistics for Engineers and the Scientists was written by and is associated to the ISBN: 9780321629111. This textbook survival guide was created for the textbook: Probability and Statistics for Engineers and the Scientists, edition: 9.

2 k p  factorial experiment
A fractional factorial experiment with k factors tested in a 2 ? p fraction with all factors tested at only two levels (settings) each

Bias
An effect that systematically distorts a statistical result or estimate, preventing it from representing the true quantity of interest.

Bivariate distribution
The joint probability distribution of two random variables.

Block
In experimental design, a group of experimental units or material that is relatively homogeneous. The purpose of dividing experimental units into blocks is to produce an experimental design wherein variability within blocks is smaller than variability between blocks. This allows the factors of interest to be compared in an environment that has less variability than in an unblocked experiment.

Box plot (or box and whisker plot)
A graphical display of data in which the box contains the middle 50% of the data (the interquartile range) with the median dividing it, and the whiskers extend to the smallest and largest values (or some deined lower and upper limits).

C chart
An attribute control chart that plots the total number of defects per unit in a subgroup. Similar to a defectsperunit or U chart.

Categorical data
Data consisting of counts or observations that can be classiied into categories. The categories may be descriptive.

Chisquare (or chisquared) 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.

Chisquare test
Any test of signiicance based on the chisquare distribution. The most common chisquare tests are (1) testing hypotheses about the variance or standard deviation of a normal distribution and (2) testing goodness of it of a theoretical distribution to sample data

Conditional mean
The mean of the conditional probability distribution of a random variable.

Consistent estimator
An estimator that converges in probability to the true value of the estimated parameter as the sample size increases.

Contingency table.
A tabular arrangement expressing the assignment of members of a data set according to two or more categories or classiication criteria

Continuous distribution
A probability distribution for a continuous random variable.

Correlation coeficient
A dimensionless measure of the linear association between two variables, usually lying in the interval from ?1 to +1, with zero indicating the absence of correlation (but not necessarily the independence of the two variables).

Cumulative distribution function
For a random variable X, the function of X deined as PX x ( ) ? that is used to specify the probability distribution.

Enumerative study
A study in which a sample from a population is used to make inference to the population. See Analytic study

Expected value
The expected value of a random variable X is its longterm average or mean value. In the continuous case, the expected value of X is E X xf x dx ( ) = ?? ( ) ? ? where f ( ) x is the density function of the random variable X.

Firstorder model
A model that contains only irstorder terms. For example, the irstorder response surface model in two variables is y xx = + ?? ? ? 0 11 2 2 + + . A irstorder model is also called a main effects model

Forward selection
A method of variable selection in regression, where variables are inserted one at a time into the model until no other variables that contribute signiicantly to the model can be found.

Frequency distribution
An arrangement of the frequencies of observations in a sample or population according to the values that the observations take on