BS3.3

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Bill Foster

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Bill Foster 12 years, 2 months ago

Created this.

Name	Status	Author	Last Modified
BS3.3	draft	Bill Foster	06/08/2020 08:42
Clodagh's copy of BS3.3 Binomial Cookies	draft	Clodagh Carroll	26/10/2023 12:19

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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	19/100
thisaswell	string	our selection contains no more
else	string	biscuits are selected at rando
thismany	integer	19
number1	integer	8
post	string	% of biscuits made by a baker
prob2	decimal	dec("0.533")
prob1	number	0.039
thatnumber	integer	1
this	string	our selection contains exactly
v	integer	0
tprob1	number	0.0392692421
tprob2	rational	2958906809572511/5551115123125783
sd	decimal	dec("1.110")

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:

This variable doesn't seem to be used anywhere.

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

a)

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

2. The expectation is given by $\operatorname{E}[X]=n\times p=\var{number1}\times \var{prob}=\var{number1*prob}$

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

b)

$\begin{eqnarray*}\operatorname{P}(X = \var{thisnumber}) &=& \dbinom{\var{number1}}{\var{thisnumber}}\times\var{prob}^{\var{thisnumber}}\times(1-\var{prob})^{\var{number1-thisnumber}}\\& =& \var{comb(number1,thisnumber)} \times\var{prob}^{\var{thisnumber}}\times\var{1-prob}^{\var{number1-thisnumber}}\\&=&\var{prob1}\end{eqnarray*}$ 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.

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

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Checkpoint description

Bill Foster 12 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: `string`

Parts

Gap-fill

a)

b)

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BS3.3

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Bill Foster 12 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: string

Parts

Gap-fill

a)

b)

Generated value: `string`