Answer:
a) The mean number of radioactive atoms that decay per day is 81.485.
b) 0% probability that on a given day, 50 radioactive atoms decayed.
Step-by-step explanation:
Poisson distribution:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

In which
x is the number of sucesses
e = 2.71828 is the Euler number
is the mean in the given interval.
a. Find the mean number of radioactive atoms that decayed in a day.
29,742 atoms decayed during 365 days, which means that:

The mean number of radioactive atoms that decay per day is 81.485.
b. Find the probability that on a given day, 50 radioactive atoms decayed.
This is P(X = 50). So

0% probability that on a given day, 50 radioactive atoms decayed.
If i'm correct you should add 0.5 mL to your 1 gallon tank, and I would say about 1.25 mL to your 2.5 gallon. It will not be extreme if you end up putting a little more in than you are supposed to. I'm not 100% because i haven't slept so my brain is being slow.
Pythagorean theorem a^2+b^2=c^2
It is B or 2. Hope this helps