(a(i))[2]
The heights of club members follow a normal distribution with mean $166\text{ cm}$ and standard deviation $10\text{ cm}$. Find the probability that a member chosen at random from the club has a height below $170\text{ cm}$.
(a(ii))[3]
With $40\%$ of the members having heights above $h\text{ cm}$, determine $h$ correct to $2$ decimal places.
(b)[3]
The random variable $X$ has a normal distribution with mean $\mu$ and standard deviation $\sigma$. If $\sigma = \frac{2}{3}\mu$, determine the probability that a value of $X$ chosen at random is positive.