(a)[3]
The random variable $X$ is distributed as $N(\mu, \sigma^2)$, with $\mu = 1.5\sigma$. A value of $X$ is selected at random. Find the probability that this selected value of $X$ is greater than $0$.
(b)[3]
The lifetime of a certain kind of torch battery is normally distributed with mean $120$ hours and standard deviation $s$ hours. It is known that $87.5\%$ of these batteries last for more than $70$ hours. Find the value of $s$.