5. The heights of a population of men are normally distributed with mean \(\mu \mathrm { cm }\) and standard deviation \(\sigma \mathrm { cm }\). It is known that \(20 \%\) of the men are taller than 180 cm and \(5 \%\) are shorter than 170 cm .
a Sketch a diagram to show the distribution of heights represented by this information.
b Find the value of \(\mu\) and \(\sigma\).
c Three men are selected at random, find the probability that they are all taller than 175 cm .
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