The heights of a population of women are normally distributed with mean \(\mu \mathrm { cm }\) and standard deviation \(\sigma \mathrm { cm }\). It is known that \(30 \%\) of the women are taller than 172 cm and \(5 \%\) are shorter than 154 cm .
Sketch a diagram to show the distribution of heights represented by this information.
Show that \(\mu = 154 + 1.6449 \sigma\).
Obtain a second equation and hence find the value of \(\mu\) and the value of \(\sigma\).
A woman is chosen at random from the population.
Find the probability that she is taller than 160 cm .