(a)[5]
The distance that tyres of a certain make can cover before replacement is needed has a normal distribution. A large survey of these tyres showed that the probability of the distance exceeding $36\,800\text{ km}$ is $0.0082$, while the probability of it exceeding $31\,000\text{ km}$ is $0.6915$. Determine the mean and standard deviation of the distribution.
(b)[3]
The random variable $X$ follows $N(\mu, \sigma^2)$, with $3\sigma = 4\mu$ and $\mu \neq 0$. Determine $P(X < 3\mu)$.