Daily sales, measured in litres, at a petrol station are normally distributed with mean $4520$ and standard deviation $560$. Determine for how many of the $365$ days in the year the daily sales are expected to exceed $3900$ litres.
At a different petrol station, daily sales are represented by $X$ litres, where $X$ follows a normal distribution with mean $m$ and standard deviation $560$. It is known that $P(X > 8000) = 0.122$. Determine the value of $m$.
Find the probability that, over fewer than $2$ of $6$ randomly selected days, daily sales at this petrol station exceed $8000$ litres.
The random variable $Y$ has a normal distribution with mean $\mu$ and standard deviation $\sigma$. If $\sigma = \frac{2}{5}\mu$, determine the probability that a randomly chosen value of $Y$ is less than $2\mu$.