 3.3.1: Area under the curve, Part I. What percent of a standard normal dis...
 3.3.2: Area under the curve, Part II. What percent of a standard normal di...
 3.3.3: Sophia who took the Graduate Record Examination (GRE) scored 160 on...
 3.3.4: In triathlons, it is common for racers to be placed into age and ge...
 3.3.5: In Exercise 3.3 we saw two distributions for GRE scores: N( = 151, ...
 3.3.6: In Exercise 3.4 we saw two distributions for triathlon times: N( = ...
 3.3.7: The average daily high temperature in June in LA is 77F with a stan...
 3.3.8: The Capital Asset Pricing Model (CAPM) is a financial model that as...
 3.3.9: Exercise 3.7 states that average daily high temperature in June in ...
 3.3.10: Heights of 10 year olds. Heights of 10 year olds, regardless of gen...
 3.3.11: Auto insurance premiums. Suppose a newspaper article states that th...
 3.3.12: The distribution of passenger vehicle speeds traveling on the Inter...
 3.3.13: Suppose weights of the checked baggage of airline passengers follow...
 3.3.14: Find the standard deviation of the distribution in the following si...
 3.3.15: Buying books on Ebay. The textbook you need to buy for your chemist...
 3.3.16: SAT scores (out of 2400) are distributed normally with a mean of 15...
 3.3.17: Below are final exam scores of 20 Introductory Statistics students....
 3.3.18: Below are heights of 25 female college students. 1 54, 2 55, 3 56, ...
 3.3.19: Is it Bernoulli? Determine if each trial can be considered an indep...
 3.3.20: With and without replacement. In the following situations assume th...
 3.3.21: Married women. The 2010 American Community Survey estimates that 47...
 3.3.22: A machine that produces a special type of transistor (a component o...
 3.3.23: A husband and wife both have brown eyes but carry genes that make i...
 3.3.24: Exercise 3.12 states that the distribution of speeds of cars travel...
 3.3.25: Data collected by the Substance Abuse and Mental Health Services Ad...
 3.3.26: The National Vaccine Information Center estimates that 90% of Ameri...
 3.3.27: We learned in Exercise 3.25 that about 70% of 1820 year olds consu...
 3.3.28: We learned in Exercise 3.26 that about 90% of American adults had c...
 3.3.29: University admissions. Suppose a university announced that it admit...
 3.3.30: Survey response rate. Pew Research reported in 2012 that the typica...
 3.3.31: ame of dreidel. A dreidel is a foursided spinning top with the Heb...
 3.3.32: Arachnophobia. A 2005 Gallup Poll found that 7% of teenagers (ages ...
 3.3.33: Exercise 3.23 introduces a husband and wife with brown eyes who hav...
 3.3.34: Sickle cell anemia is a genetic blood disorder where red blood cell...
 3.3.35: In the game of roulette, a wheel is spun and you place bets on wher...
 3.3.36: In a multiple choice quiz there are 5 questions and 4 choices for e...
 3.3.37: The formula for the number of ways to arrange n objects is n! = n (...
 3.3.38: While it is often assumed that the probabilities of having a boy or...
 3.3.39: Calculate the following probabilities and indicate which probabilit...
 3.3.40: Calculate the following probabilities and indicate which probabilit...
 3.3.41: For a sociology class project you are asked to conduct a survey on ...
 3.3.42: A notsoskilled volleyball player has a 15% chance of making the s...
 3.3.43: Customers at a coee shop. A coee shop serves an average of 75 custo...
 3.3.44: A very skilled court stenographer makes one typographical error (ty...
Solutions for Chapter 3: Distributions of Random Variables
Full solutions for OpenIntro Statistics  3rd Edition
ISBN: 9781943450039
Solutions for Chapter 3: Distributions of Random Variables
Get Full SolutionsSince 44 problems in chapter 3: Distributions of Random Variables have been answered, more than 41303 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 3: Distributions of Random Variables includes 44 full stepbystep solutions. OpenIntro Statistics was written by and is associated to the ISBN: 9781943450039. This textbook survival guide was created for the textbook: OpenIntro Statistics, edition: 3.

2 k factorial experiment.
A full factorial experiment with k factors and all factors tested at only two levels (settings) each.

Bernoulli trials
Sequences of independent trials with only two outcomes, generally called “success” and “failure,” in which the probability of success remains constant.

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

Biased estimator
Unbiased estimator.

Binomial random variable
A discrete random variable that equals the number of successes in a ixed number of Bernoulli trials.

Bivariate normal distribution
The joint distribution of two normal random variables

Comparative experiment
An experiment in which the treatments (experimental conditions) that are to be studied are included in the experiment. The data from the experiment are used to evaluate the treatments.

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

Continuous uniform random variable
A continuous random variable with range of a inite interval and a constant probability density function.

Correction factor
A term used for the quantity ( / )( ) 1 1 2 n xi i n ? = that is subtracted from xi i n 2 ? =1 to give the corrected sum of squares deined as (/ ) ( ) 1 1 2 n xx i x i n ? = i ? . The correction factor can also be written as nx 2 .

Covariance matrix
A square matrix that contains the variances and covariances among a set of random variables, say, X1 , X X 2 k , , … . The main diagonal elements of the matrix are the variances of the random variables and the offdiagonal elements are the covariances between Xi and Xj . Also called the variancecovariance matrix. When the random variables are standardized to have unit variances, the covariance matrix becomes the correlation matrix.

Critical region
In hypothesis testing, this is the portion of the sample space of a test statistic that will lead to rejection of the null hypothesis.

Curvilinear regression
An expression sometimes used for nonlinear regression models or polynomial regression models.

Eficiency
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.

Erlang random variable
A continuous random variable that is the sum of a ixed number of independent, exponential random variables.

Error mean square
The error sum of squares divided by its number of degrees of freedom.

Event
A subset of a sample space.

Exponential random variable
A series of tests in which changes are made to the system under study

Ftest
Any test of signiicance involving the F distribution. The most common Ftests 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.

Harmonic mean
The harmonic mean of a set of data values is the reciprocal of the arithmetic mean of the reciprocals of the data values; that is, h n x i n i = ? ? ? ? ? = ? ? 1 1 1 1 g .