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Solutions for Chapter 6.2: The Binomial Probability Distribution

Full solutions for Statistics: Informed Decisions Using Data | 5th Edition

ISBN: 9780134133539

Solutions for Chapter 6.2: The Binomial Probability Distribution

Solutions for Chapter 6.2
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ISBN: 9780134133539

Summary of Chapter 6.2: The Binomial Probability Distribution

Determine whether a probability experiment is a binomial experiment. Compute probabilities of binomial experiments. Compute the mean and standard deviation of a binomial random variable. Graph a binomial probability distribution

This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Statistics: Informed Decisions Using Data, edition: 5. Since 60 problems in chapter 6.2: The Binomial Probability Distribution have been answered, more than 17513 students have viewed full step-by-step solutions from this chapter. Chapter 6.2: The Binomial Probability Distribution includes 60 full step-by-step solutions. Statistics: Informed Decisions Using Data was written by and is associated to the ISBN: 9780134133539.

Key Statistics Terms and definitions covered in this textbook
• Additivity property of x 2

If two independent random variables X1 and X2 are distributed as chi-square with v1 and v2 degrees of freedom, respectively, Y = + X X 1 2 is a chi-square random variable with u = + v v 1 2 degrees of freedom. This generalizes to any number of independent chi-square random variables.

• Arithmetic mean

The arithmetic mean of a set of numbers x1 , x2 ,…, xn is their sum divided by the number of observations, or ( / )1 1 n xi t n ? = . The arithmetic mean is usually denoted by x , and is often called the average

• Axioms of probability

A set of rules that probabilities deined on a sample space must follow. See Probability

• Bivariate normal distribution

The joint distribution of two normal random variables

• Central limit theorem

The simplest form of the central limit theorem states that the sum of n independently distributed random variables will tend to be normally distributed as n becomes large. It is a necessary and suficient condition that none of the variances of the individual random variables are large in comparison to their sum. There are more general forms of the central theorem that allow ininite variances and correlated random variables, and there is a multivariate version of the theorem.

• 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.

• Continuous random variable.

A random variable with an interval (either inite or ininite) of real numbers for its range.

• Correlation

In the most general usage, a measure of the interdependence among data. The concept may include more than two variables. The term is most commonly used in a narrow sense to express the relationship between quantitative variables or ranks.

• 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).

• Critical value(s)

The value of a statistic corresponding to a stated signiicance level as determined from the sampling distribution. For example, if PZ z PZ ( )( .) . ? =? = 0 025 . 1 96 0 025, then z0 025 . = 1 9. 6 is the critical value of z at the 0.025 level of signiicance. Crossed factors. Another name for factors that are arranged in a factorial experiment.

• Defect concentration diagram

A quality tool that graphically shows the location of defects on a part or in a process.

• Deming

W. Edwards Deming (1900–1993) was a leader in the use of statistical quality control.

• Discrete random variable

A random variable with a inite (or countably ininite) range.

• Error propagation

An analysis of how the variance of the random variable that represents that output of a system depends on the variances of the inputs. A formula exists when the output is a linear function of the inputs and the formula is simpliied if the inputs are assumed to be independent.

• Error variance

The variance of an error term or component in a model.

• Exponential random variable

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

• Factorial experiment

A type of experimental design in which every level of one factor is tested in combination with every level of another factor. In general, in a factorial experiment, all possible combinations of factor levels are tested.

• False alarm

A signal from a control chart when no assignable causes are present

• Gamma random variable

A random variable that generalizes an Erlang random variable to noninteger values of the parameter r

• Generating function

A function that is used to determine properties of the probability distribution of a random variable. See Moment-generating function