Calculating how many 100s are needed to reach target goal

There sure is, but it starts with algebra.

definition of average: average=sum/count (you should remember this from secondary school if not primary school)
current form: average=sum/count=9.34/10
new average: average=sum/count=(9.34+x*1)/(10+x)>=0.95
Solve inequality for x. At this point, I will assume you know how to solve that for x. If you need an algebra refresher: http://www.purplemath.com/modules/solvelin3.htm
Translate that formula into Excel to find the number of 100% scores you need to get above 95%.

If you get stuck, let us know where you get stuck and we'll help you through it.

3.2 is approximately correct, though x needs to be an integer, so you can't leave it there. 3 100% will yield an average of 94.88%, which is just below 95%. You would need to decide if that is close enough, or if you would prefer to round the result up to 4.

So far, we really haven't done any Excel, yet. Let's finish the algebra, then the Excel will be easier.

rather than solve this for the specific case, can you solve this for a more generic case (all variables, no numbers)?

target average: average=(current sum+1*x)/(current count+x)>=0.95
solve for x: x=(target average*current count-current sum)/(1-target average)
You already have cells with current count and target average. If you added a cell to count current sum, it should be straightforward to program that formula into a cell. Then, as I suggested earlier, decide if you need to round up to be sure you are always above 95.000%