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rebelmaths

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Given a random variable $X$  normally distributed as $\\operatorname{N}(m,\\sigma^2)$ find probabilities $P(X \\gt a),\\; a \\gt m;\\;\\;P(X \\lt b),\\;b \\lt m$.

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

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

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

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

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

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3.

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

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

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Probability = ?[[0]](to 2  decimal places)

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

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Probability = ?[[1]](to 2  decimal places)

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Find the probability that in a particular week the {amount} is between {lower}{units1} and {upper} {units1}:

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Probability = ?[[2]](to 2  decimal places)

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