Calculate probabilities from a normal distribution,

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Newcastle University Mathematics and Statistics

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Newcastle University Mathematics and Statistics 9 years, 3 months ago

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Question statement

The {amount}, $X$, of {stuff} is normally distributed with mean {m}{units1} 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	945
lower	integer	775
p1	number	0.9126320884
m	integer	850
s	integer	70
p	number	0.8580116141
amount	string	electricity consumption
stuff	string	a frozen foods warehouse each
tol	number	0.0001
prob2	number	0.0874
prob1	number	0.1420

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Name

Data type

Value

xxxxxxxxxx
 
"k Wh"

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Description

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

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Generated value: `string`

k Wh

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1. Gap Gap 0. Number entry
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2. Gap Gap 1. Number entry
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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 4 decimal places)

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

Probability = Gap 1.(to 4 decimal places)

Advice

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

$\simplify[all,!collectNumbers]{P(X < {lower}) = P(Z < ({lower} -{m}) / {s}) = P(Z < {lower-m}/{s}) = 1 -P(Z < {m-lower}/{s})} = 1 -\var{p} = \var{precround(1 -p,4)}$ to 4 decimal places.

Here the probability could have been looked up from normal CDF tables. Alternatively we can simply do the whole

calculation in R by typing $\operatorname{pnorm}(\var{lower},\var{m},\var{s})$.

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

$\simplify[all,!collectNumbers]{P(X > {upper}) = P(Z > ({upper} -{m}) / {s}) = P(Z > {upper-m}/{s}) = 1 -P(Z < {upper-m}/{s})} = 1-\var{p1} = \var{precround(1 -p1,4)}$ to 4 decimal places.

Here the probability could have been looked up from normal CDF tables. Alternatively we can

simply do the whole calculation in R by typing 1 - pnorm({upper},{m},{s}).

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Calculate probabilities from a normal distribution,

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Newcastle University Mathematics and Statistics 9 years, 3 months ago

Error in variable testing condition

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Generated value: `string`

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Calculate probabilities from a normal distribution,

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Newcastle University Mathematics and Statistics 9 years, 3 months ago

Error in variable testing condition

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Warning

Generated value: string

Parts

Gap-fill

Generated value: `string`