Clodagh's copy of Calculate probabilities from a normal distribution

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Question 1

The electricity consumption, $X$ , of a frozen foods warehouse each week in the summer months is normally distributed with mean 750k Wh and standard deviation 80k Wh.

Find the probability that in a particular week the electricity consumption is less than 685 k Wh:

Probability = ?Expected answer:(to 2 decimal places)

Find the probability that in a particular week the electricity consumption is greater than 830 k Wh:

Probability = ?Expected answer:(to 2 decimal places)

Find the probability that in a particular week the electricity consumption is between 685k Wh and 830 k Wh:

Probability = ?Expected answer:(to 2 decimal places)

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Advice

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

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

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

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

$\simplify[all,!collectNumbers]{P({lower} < X < {upper}) = P(X < {upper})-P(X < {lower})}=P(Z<\var{zupper})-P(Z<-\var{zlower}) =\var{p1}-\var{p2} = \var{prob3}$ to 2 decimal places.

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Clodagh's copy of Calculate probabilities from a normal distribution

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