Normally distributed rain drops problem About 50% of raindrops land downtown, downtown is a perfectly circular space around the city centre. Assuming the coordinates of the raindrops are independent and distributed according to the standard normal about the city centre. What is the percentage of rain drops that land within a radius twice that of downtown? 
Since around 50% of the raindrops land downtown, clearly the percentage landing within a radius twice that of downtown must be less than or equal to 50, but beyond this I am not sure how to approach/solve this problem, can someone help? Thanks! 

Let us look at a normal distribution in one dimension first, then proceed into two dimensions.
According to your statement, 50% of the raindrops land in downtown. Without loss of generality, let's assume that 'downtown' is one kilometer in radius. Let's model that in one dimension:
$$Pr(\mu-n\sigma\leq X\leq\mu+n\sigma)=\Phi(n)-\Phi(-n)=0.5$$
In this case, looking at a z-table gives $0.67<n<0.68$. Now, we'll double n to find the standard deviation for the raindrops that land exactly two kilometers from downtown. We get in that case $n\approx1.35$. Now we plug that back in:
$$Pr(\mu-2n\sigma\leq X\leq\mu+2n\sigma)\approx\Phi(1.35)-\Phi(-1.35)\approx0.823$$
again using the z-table.
Now, since we are talking about two dimensions rather than one, we square the resultant probability to obtain $(0.823)^2\approx0.677$.
Hope this works! Not sure if I'm correct, I'm no expert. (Not 100% confident about the last step.)
