David's copy of Calculate probabilities from normal distribution,

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David Wishart

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David Wishart 6 years, 11 months ago

Created this as a copy of Calculate probabilities from normal distribution, .

Name	Status	Author	Last Modified
Calculate probabilities from normal distribution,	draft	Newcastle University Mathematics and Statistics	20/11/2019 14:50
Clodagh's copy of Julie's copy of Calculate probabilities from normal distribution,	draft	Clodagh Carroll	10/10/2016 09:59
Julie's copy of Clodagh's copy of Julie's copy of Calculate probabilities from normal distribution,	draft	Julie Crowley	07/03/2017 14:56
David's copy of Calculate probabilities from normal distribution,	draft	David Wishart	20/04/2018 17:42

There are 6 other versions that do you not have access to.

Question statement

The {amount}, $X$, of {stuff} is normally distributed with mean {m}k and standard deviation {s}{units1}.

i.e. \[X \sim \operatorname{N}(\var{m},\var{s}^2)\]

Give any introductory information the student needs.

			Name	Type	Generated Value

units1	string	k Wh
upper	integer	1320
lower	integer	1140
p1	number	0.9082
m	integer	1200
amount	string	electricity consumption
zupper	decimal	dec("1.33")
p	number	0.7486
s	integer	90
stuff	string	a frozen foods warehouse each
tol	number	0.01
zlower	decimal	dec("0.67")
prob2	number	0.09
prob1	number	0.25

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
"k Wh"

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`

k Wh

Parts

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.

Find the probability that in a particular week the {amount} is less than {lower} {units1}:

Probability = ?Gap 0.(to 2 decimal places)

Find the probability that in a particular week the {amount} is greater than {upper} {units1}:

Probability = ?Gap 1.(to 2 decimal places)

Advice

1. Converting to $\operatorname{N}(0,1)$

$\simplify[all,!collectNumbers]{P(X < {lower}) = P(Z < ({lower} -{m}) / {s}) =1 -P(Z < {m-lower}/{s})} = 1-P(z<\var{zlower})=1 -\var{p} = \var{prob1}$ to 2 decimal places.

2. Converting to $\operatorname{N}(0,1)$

$\simplify[all,!collectNumbers]{P(X > {upper}) = P(Z > ({upper} -{m}) / {s}) = 1 -P(Z < {upper-m}/{s})} = 1-P(z<\var{zupper})=1-\var{p1} = \var{prob2}$ to 2 decimal places.

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Part	Test	Passed?
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David's copy of Calculate probabilities from normal distribution,

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Taxonomy: mathcentre

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David Wishart 6 years, 11 months ago

Error in variable testing condition

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Generated value: `string`

Parts

Gap-fill

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Error

David's copy of Calculate probabilities from normal distribution,

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

David Wishart 6 years, 11 months ago

Error in variable testing condition

Error

Warning

Generated value: string

Parts

Gap-fill

Generated value: `string`