# QB/d Bell.binomial

< QB
Jump to navigation Jump to search

• Quizbank now resides on MyOpenMath at https://www.myopenmath.com (although I hope Wikiversity can play an important role in helping students and teachers use these questions!)
• At the moment, most of the physics questions have already been transferred. To see them, join myopenmath.com as a student, and "enroll" in one or both of the following courses:
• Quizbank physics 1 (id 60675)
• Quizbank physics 2 (id 61712)
• Quizbank astronomy (id 63705)

The enrollment key for each course is 123. They are all is set to practice mode, giving students unlimited attempts at each question. Instructors can also print out copies of the quiz for classroom use. If you have any problems leave a message at user talk:Guy vandegrift.

-

See special:permalink/1882674 for a wikitext version of this quiz.

### LaTexMarkup begin

%[[File:Quizbankqb_{{SUBPAGENAME}}.pdf|thumb|See[[:File:Quizbankqb_{{SUBPAGENAME}}.pdf]]]]
%CurrentID: {{REVISIONID}}
%PDF: [[:File:Quizbankqb_{{SUBPAGENAME}}.pdf]]%Required images: [[file:Wikiversity-logo-en.svg|45px]]

%This code creates both the question and answer key using \newcommand\mytest
%%%    EDIT QUIZ INFO  HERE   %%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcommand{\quizname}{QB/d_Bell.binomial}

\newcommand{\quiztype}{conceptual}%[[Category:QB/conceptual]]
%%%%% PREAMBLE%%%%%%%%%%%%
\newif\ifkey %estabkishes Boolean ifkey to turn on and off endnotes

\documentclass[11pt]{exam}
\RequirePackage{amssymb, amsfonts, amsmath, latexsym, verbatim,
xspace, setspace,datetime}
\RequirePackage{tikz, pgflibraryplotmarks, hyperref}
\usepackage[left=.5in, right=.5in, bottom=.5in, top=.75in]{geometry}
\usepackage{endnotes, multicol,textgreek} %
\usepackage{graphicx} %
\singlespacing %OR \onehalfspacing OR \doublespacing
\parindent 0ex % Turns off paragraph indentation
\hypersetup{ colorlinks=true, urlcolor=blue}
% BEGIN DOCUMENT
\begin{document}
\title{d\_Bell.binomial}
\author{The LaTex code that creates this quiz is released to the Public Domain\\
Attribution for each question is documented in the Appendix}
\maketitle
\begin{center}
\includegraphics[width=0.15\textwidth]{666px-Wikiversity-logo-en.png}
\\Latex markup at\\
\footnotesize{ \url{https://en.wikiversity.org/wiki/special:permalink/1882674}}
\end{center}
\begin{frame}{}
\begin{multicols}{3}
\tableofcontents
\end{multicols}
\end{frame}
\pagebreak\section{Quiz}
\keytrue
\printanswers
\begin{questions}\keytrue

\question The normal distribution (often called a "bell curve") is never skewed\ifkey\endnote{CC0 [[user:Guy vandegrift]] placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1882674}}}\fi
\begin{choices}
\CorrectChoice True
\choice False
\end{choices}

\question The normal distribution (often called a "bell curve") is usually skewed\ifkey\endnote{CC0 [[user:Guy vandegrift]] placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1882674}}}\fi
\begin{choices}
\choice True
\CorrectChoice False
\end{choices}

\question By definition, a skewed distribution\ifkey\endnote{CC0 [[user:Guy vandegrift]] placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1882674}}}\fi
\begin{choices}
\choice is broader than an unskewed distribution
\choice includes negative values of the observed variable
\choice is a "normal" distribution
\CorrectChoice is asymmetric about its peak value
\choice contains no outliers
\end{choices}

\question The binomial distribution results from observing n outcomes, each having a probability p of "success"\ifkey\endnote{CC0 [[user:Guy vandegrift]] placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1882674}}}\fi
\begin{choices}
\CorrectChoice True
\choice False
\end{choices}

\question What is the probability of success, p, for a binary distribution using a six-sided die, with success defined as "two"?\ifkey\endnote{CC0 [[user:Guy vandegrift]] placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1882674}}}\fi
\begin{choices}
\choice 3/6
\choice 2/6
\CorrectChoice 1/6
\choice 5/6
\choice 4/6
\end{choices}

\question What is the probability of success, p, for a binary distribution using a six-sided die, with success defined as anything but "two"?\ifkey\endnote{CC0 [[user:Guy vandegrift]] placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1882674}}}\fi
\begin{choices}
\choice 3/6
\choice 2/6
\choice 1/6
\CorrectChoice 5/6
\choice 4/6
\end{choices}

\question What is the probability of success, p, for a binary distribution using a six-sided die, with success defined as either a "two" or a "three"?\ifkey\endnote{CC0 [[user:Guy vandegrift]] placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1882674}}}\fi
\begin{choices}
\choice 3/6
\CorrectChoice 2/6
\choice 1/6
\choice 5/6
\choice 4/6
\end{choices}

\question How would you describe the "skew" of a binary distribution?\ifkey\endnote{CC0 [[user:Guy vandegrift]] placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1882674}}}\fi
\begin{choices}
\CorrectChoice The binary distribution is always skewed, but has little skew for a large number of trials n.
\choice The binary distribution is always skewed, but has little skew for a small number of trials n.
\choice The binary distribution is never skewed if it is a true binary distribution.
\choice Distributions are never skewed.  Only experimental measurements of them are skewed.
\choice None of these are true.
\end{choices}

\question For a binomial distribution with n trials, the variance is \textsigma\ \textsuperscript{2}=np(1-p). If 90 trials are observed, then 68\% of the time the observed number of positive outcomes will fall within $$\pm$$\_\_\_ of the expected value if p=.11 is the probability of a positive outcome. Make the approximation that this binomial distribution is approximately a Gaussian (normal) distribution).\ifkey\endnote{CCO [[user:Guy vandegrift]] placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1882674}}}\fi
\begin{choices}
\choice 6
\choice 18
\CorrectChoice 3
\choice 9
\choice 1
\end{choices}

\question For a binomial distribution with n trials, the variance is \textsigma\ \textsuperscript{2}=np(1-p). If 40 trials are observed, then 68\% of the time the observed number of positive outcomes will fall within $$\pm$$\_\_\_ of the expected value if p=.11 is the probability of a positive outcome. Make the approximation that this binomial distribution is approximately a Gaussian (normal) distribution).\ifkey\endnote{CCO  [[user:Guy vandegrift]] placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1882674}}}\fi
\begin{choices}
\choice 6
\choice 18
\choice 3
\choice 9
\CorrectChoice 2
\end{choices}

\question For a binomial distribution with n trials, the variance is \textsigma\ \textsuperscript{2}=np(1-p). If 40 trials are made and p=.11, the expected number of positive outcomes is\_\_. Make the approximation that this binomial distribution is approximately a Gaussian (normal) distribution.\ifkey\endnote{CCO [[user:Guy vandegrift]] placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1882674}}}\fi
\begin{choices}
\CorrectChoice 4.4
\choice 2.2
\choice 9.9
\choice 3.3
\choice 1.1
\end{choices}

\question For a binomial distribution with n trials, the variance is \textsigma\ \textsuperscript{2}=np(1-p). If 90 trials are made and p=.11, the expected number of positive outcomes is\_\_. Make the approximation that this binomial distribution is approximately a Gaussian (normal) distribution.\ifkey\endnote{CCO [[user:Guy vandegrift]] placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1882674}}}\fi
\begin{choices}
\choice 2.2
\CorrectChoice 9.9
\choice 3.3
\choice 1.1
\end{choices}

\question Recall that only 4.6\% of the outcomes for a normal distribution lie outside of two standard deviations from the mean, and approximate the binomial distribution as normal for large numbers.  If the variance is  \textsigma\ \textsuperscript{2}=np(1-p) where n is the number of trials and p=.11 is the probability of a positive outcome for 40 trials, roughly 98\% of the outcomes will be smaller than approximately \_\_\ifkey\endnote{CC0 [[user:Guy vandegrift]] placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1882674}}}\fi
\begin{choices}
\choice 6
\CorrectChoice 8
\choice 12
\choice 16
\choice 22
\end{choices}

\question Recall that only 4.6\% of the outcomes for a normal distribution lie outside of two standard deviations from the mean, and approximate the binomial distribution as normal for large numbers.  If the variance is  \textsigma\ \textsuperscript{2}=np(1-p) where n is the number of trials and p=.11 is the probability of a positive outcome for 90 trials, roughly 98\% of the outcomes will be smaller than approximately \_\_\ifkey\endnote{CC0 [[user:Guy vandegrift]] placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1882674}}}\fi
\begin{choices}
\choice 6
\choice 8
\choice 12
\CorrectChoice 16
\choice 22
\end{choices}

\question A local college averages 2500 new incoming students each year.  Suppose the pool of potential high school graduates in the local area is so large that the probability of a given student selecting this college is small, and assume a variance of \textsigma\ \textsuperscript{2} equal to p(1-p).  What standard deviation would you expect in the yearly total of new enrollees, assuming nothing changes in this population from year to year? \ifkey\endnote{CC0 [[user:Guy vandegrift]] placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1882674}}}\fi
\begin{choices}
\CorrectChoice 50
\choice 150
\choice 500
\choice 200
\choice 250
\end{choices}

\question A local college averages 1600 new incoming students each year.  Suppose the pool of potential high school graduates in the local area is so large that the probability of a given student selecting this college is small, and assume a variance of \textsigma\ \textsuperscript{2} equal to p(1-p).  What standard deviation would you expect in the yearly total of new enrollees, assuming nothing changes in this population from year to year? \ifkey\endnote{CC0 [[user:Guy vandegrift]] placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1882674}}}\fi
\begin{choices}
\choice 16
\choice 160
\CorrectChoice 40
\choice 10
\choice 32
\end{choices}
\end{questions}

\newpage
\section{Attribution}
\theendnotes
\end{document}