A statistics problem involves:
Lengths of a certain type of carrot have a normal distribution with mean 14.2 cm and standard deviation 3.6 cm. (i) 8% of carrots are shorter than c cm. Find the value of c.
I know that the z statistic would be $\frac{c-\mu}\sigma$. In the mark scheme, it simply states that z=–1.406 without any explanation as to how this was reached. I assume it had something to do with the 8%. How do I reach this?
I would say
$\Phi(\frac{c-\mu}\sigma)=0.08\Rightarrow \frac{c-\mu}\sigma =\Phi^{-1}(0.08)=-1.406$
$\Phi(u)=\,\,$ distribution function of the standard normal distribution $N(0,1)$
You'll find in the tables N(0,1), in Ecxel (function "=NORMSINV(0,08)) etc.