math thesis

For the past several weeks, I've collected all my change and tossed it into a container. During this collection process I was careful not to use any change during the day .. merely to add the coins to the pile as randomly as they arrived.

Today, my container overflowed, so I can stop my experiment. Here's the tally:

244 pennies  (1c)
059 nickels  (5c)
135 dimes    (10c)
140 quarters (25c)

My question: given random numbers and all that rot, is this an expected distribution?

I fully expect hordes of math majors (eager to complete their doctoral thesis) will apply themselves to this problem, post haste.

And now, we wait.

Extra credit: This container of change equals $53.89 .. what is the probability that future containers will be within ten (10) percent of today's total?