I was given the following question from a friend of mine and I can't seem to understand it to well:
A squadron of 10 bombers attempts to destroy an ammunition depot. The fighter jet flies in the horizontal direction. The aiming point is the center of the depot. The point of impact is assumed to be a normally distributed around the aiming point $(60,0)$ with a standard deviation $\sigma$ of $200$ yards in the horizontal direction and $100$ yards in the vertical direction. Simulate the operation and estimate the number of bombs on target.
The middle two corners of the following ammunition depot are $(-150,0)$ and $(270,0)$. $X$~Normal (mean $= 60, \sigma = 200$) and $Y$~Normal (mean $=0,\sigma = 100$).
The picture above is a diagram of the ammunition depot.
I don't have a strong background in statistics to fully understand how the normal distribution is being applied here. I am somewhat familiar with Monte Carlo Method, but I have only used it as an alternative to solving integrals numerically.
My idea was to just define the region above using the following equations: \begin{array} ` y_1 = 120 & & -210\leq x \leq 210\\ y_2 = -120 & & -210\leq x \leq 210\\ y_3 = 2x-540 & & 210\leq x \leq 270\\ y_4 = -2x+540 & & 210\leq x \leq 270\\ y_5 = 2x+300 & & -210\leq x \leq -150\\ y_6 = -2x-300 & & -210\leq x \leq -150\\ \end{array} Then randomly generate points that represent where the projectiles land. If the projectiles (coordinates in this case) landed within the boundary I specified, then I would mark it as a hit; otherwise, a miss. However, I do not know if this is sufficient since it does not incorporate the distribution (at least not that I know of).
Thank you for your time and have a wonderful day.