Calculate probabilities from a binomial distribution

Error

There was an error loading the page.

Contributors

Newcastle University Mathematics and Statistics

Feedback

From users who are not members of Content created by Newcastle University :

Ben Parker

said

Needs to be tested

4 years, 2 months ago

History

○

Ben Parker 4 years, 2 months ago

Gave some feedback: Needs to be tested

○

Ben Parker 4 years, 2 months ago

Gave some feedback: Ready to use

○

Newcastle University Mathematics and Statistics 9 years, 2 months ago

Created this.

There is only one version of this question that you have access to.

There are 8 other versions that do you not have access to.

Question statement

{pre} $\var{thismany}$ {post}

{something} $\var{number1}$ {else}

Give any introductory information the student needs.

			Name	Type	Generated Value

pre	string
descx1	string	number of chocolate chip cooki
something	string
thisnumber	integer	4
what	string	daily sales.
things	string	chocolate chip cookies.
descx	string	the number of chocolate chip c
tol	number	0.001
prob	rational	3/20
thisaswell	string	our selection contains no more
else	string	biscuits are selected at rando
thismany	integer	15
number1	integer	6
post	string	% of biscuits made by a baker
prob2	number	0.776
prob1	number	0.005
thatnumber	integer	1
this	string	our selection contains exactly
v	integer	0
tprob1	number	0.0054864844
tprob2	number	0.7764842969
sd	decimal	dec("0.875")

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
' '

JME function reference

Description

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `string`

→ Used by:

Statement

Parts

Part a) Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add
3. Gap Gap 2. Number entry
  Add
4. Gap Gap 3. Number entry
  Add
Part b) Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add

Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

Assuming a binomial distribution for $X$ , {descX}, write down the values of $n$ and $p$.

$X \sim \operatorname{Bin}(n,p)$

$n=\; $?Gap 0. $p=\;$?Gap 1.

Find $\operatorname{E}[X]$ the expected {descX1}

$\operatorname{E}[X]=$?Gap 2.

Find the standard deviation for the {descX1}

Standard deviation = ? Gap 3. (to 3 decimal places).

Advice

1. $X \sim \operatorname{Bin}(\var{number1},\var{prob})$, so $n= \var{number1},\;\;p=\var{prob}$.

2. The expected number (or mean) is given by $\operatorname{E}[X]=n\times p=\var{number1}\times \var{prob}=\var{number1*prob}$

3. $\operatorname{SD}(X)=\sqrt{\operatorname{Var}(X)}=\sqrt{n\times p \times (1-p)}=\sqrt{\var{number1}\times \var{prob} \times \var{1-prob}}=\var{sd}$ to 3 decimal places.

1. \[ \begin{eqnarray*}\operatorname{P}(X = \var{thisnumber}) &=& ^\var{number1}C_\var{thisnumber}\times\var{prob}^{\var{thisnumber}}\times\var{1-prob}^{\var{number1}-\var{thisnumber}}\\&=& \var{comb(number1,thisnumber)} \times\var{prob}^{\var{thisnumber}}\times\var{1-prob}^{\var{number1-thisnumber}}\\&=&\var{prob1}\end{eqnarray*} \] to 3 decimal places.

\[ \begin{eqnarray*}\operatorname{P}(X \leq \var{thatnumber})& =& \simplify[all,!collectNumbers]{P(X = 0) + P(X = 1) + {v}*P(X = 2)}\\& =& \simplify[zeroFactor,zeroTerm,unitFactor]{{1 -prob} ^ {number1}+ {number1} *{prob} *{1 -prob} ^ {number1 -1} + {v} * ({number1} * {number1 -1}/2)* {prob} ^ 2 *( {1 -prob} ^ {number1 -2})}\\& =& \var{prob2}\end{eqnarray*} \]

to 3 decimal places.

Give a worked solution to the whole question.

Use this tab to check that this question works as expected.

There was an error which means the tests can't run:

Part	Test	Passed?
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet

This question is used in the following exams:

Quantitative Methods for Business Management by Newcastle University Mathematics and Statistics in Content created by Newcastle University.
Binomial Distribution by Gareth Woods in Gareth's workspace.
sample test by Gill McCartney in Gill's workspace.
gills numas try by Gill McCartney in Gill's workspace.
reassessment MA1606 by Xiaochuan Yang in Xiaochuan's workspace.
CL2603StatsWeek1 by Ben Parker in Ben's workspace.
MA5636 Week2 by Ben Parker in Ben's workspace.

Loading...

Error

Calculate probabilities from a binomial distribution

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Ben Parker 4 years, 2 months ago

Ben Parker 4 years, 2 months ago

Newcastle University Mathematics and Statistics 9 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: `string`

Parts

Gap-fill

Loading...

Error

Calculate probabilities from a binomial distribution

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Ben Parker 4 years, 2 months ago

Ben Parker 4 years, 2 months ago

Newcastle University Mathematics and Statistics 9 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: string

Parts

Gap-fill

Generated value: `string`