Poisson (sales)

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Julie Crowley

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Ready to use

8 years, 11 months ago

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Julie Crowley 8 years, 7 months ago

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Julie Crowley 8 years, 11 months ago

Gave some feedback: Ready to use

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Julie Crowley 9 years, 2 months ago

Created this as a copy of BS3.2 Poisson (sales).

Name	Status	Author	Last Modified
BS3.2	draft	Bill Foster	06/08/2020 08:42
Poisson (sales)	Ready to use	Julie Crowley	21/03/2024 12:43
Alex's copy of Poisson (sales)	draft	Alex Van den Hof	31/03/2017 11:40
Brad's copy of Poisson (sales)	draft	Brad Allison	13/06/2019 12:48

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Question statement

{pre} $\var{thismany}$ .

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

The Poisson distribution formula: $P(r)=\frac{\lambda^re^{-\lambda}}{r!}$ or $P(r)=e^{-\lambda}\left[\frac{\lambda^r}{r!}\right]$

Give any introductory information the student needs.

			Name	Type	Generated Value

pre	string	The mean number of sales per d
what	string	daily sales.
this	string	a randomly selected employee m
things	string	sales.
number1	integer	2
descx	string	the number of sales per day
else	string	per day.
thismany	integer	5
something	string	Employees receive a warning if
tol	number	0.001
v	integer	0
tprob1	number	0.1754673698
sd	number	2.236
tprob2	number	0.040427682
prob2	number	0.040
thisnumber	integer	4
thisaswell	string	a randomly selected employee r
prob1	number	0.175

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
"The mean number of sales per day at a telecommunications centre is "

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`

The mean number of sales per day at a telecommunications centre is

This variable doesn't seem to be used anywhere.

Parts

Part a) Gap-fill
1. Gap 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 Poisson distribution for {descX}, write down the value of $\lambda$ .

$\lambda =$ Unnamed gap?

Advice

1. $X \sim \operatorname{Poisson}(\var{thismany})$ , so $\lambda = \var{thismany}$ .

Remember that for a Poisson random variable:

$\begin{align} \operatorname{P}(X=x)&=\dfrac{\lambda^x\times e^{-\lambda}}{x!}\\ \end{align}$

$\begin{eqnarray*}\operatorname{P}(X = \var{thisnumber}) &=& \frac{\var{thismany} ^ {\var{thisnumber}}e ^ { -\var{thismany}}} {\var{thisnumber}!}\\& =& \var{prob1} \end{eqnarray*}$ to 3 decimal places.

2. If an employee receives a warning then he or she must have sold less than {number1}.

Hence we need to find :

$\begin{eqnarray*}\operatorname{P}(X < \var{number1})& =& \simplify[all,!collectNumbers]{P(X = 0) + P(X = 1) + {v}*P(X = 2)}\\& =& \simplify[all,!collectNumbers]{e ^ { -thismany} + {thismany} * e ^ { -thismany} + {v} * (({thismany} ^ 2 * e ^ { -thismany}) / 2)} \\&=& \var{prob2} \end{eqnarray*}$

to 3 decimal places.

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Part	Test	Passed?
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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

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Julie Crowley 8 years, 7 months ago

Julie Crowley 8 years, 11 months ago

Julie Crowley 9 years, 2 months ago

Error in variable testing condition

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Generated value: `string`

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Poisson (sales)

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Julie Crowley 8 years, 7 months ago

Julie Crowley 8 years, 11 months ago

Julie Crowley 9 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: string

Parts

Gap-fill

Generated value: `string`