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! 

I believe you can use standard z-tables (e.g. https://en.wikipedia.org/wiki/Standard_normal_table) to work out the various percentages for the radius in question.  The z-table will tell you the probability contained by the standard normal curve from 0 to whatever z-value you choose.  Now, if you make the equivalence of rain percentage to probability and z to radius, then you should be able to solve the problem.  
For example, if you look at the z-table for the standard normal, you will see that the z-value for 0.25 (25% - remember this is going to be 1/2 the total 50% because it is measured from the center), is about z=0.68.  Now, if you double this (double the radius), you will get $z=2(0.68)=1.36$.  This z-value corresponds to 0.413 or 41.3%.  Then, you'll need to double this to get 82.6% which I believe should correspond to the final answer.  
I hope this helps.
