(a)[4]
Determine the probability that a male leopard chosen at random from this region has a weight between $46\text{ kg}$ and $62\text{ kg}$.
(b)[3]
Female leopard weights in this region are normally distributed with mean $42\text{ kg}$ and standard deviation $\sigma\text{ kg}$. It is known that $25\%$ of female leopards in the region weigh less than $36\text{ kg}$. Find the value of $\sigma$.
(c)[4]
The weight distributions for male and female leopards are independent of one another. A male leopard and a female leopard are each selected at random. Find the probability that both of these leopards weigh less than $46\text{ kg}$.