Consider an experiment that consists of counting the number of alpha particles g
ID: 3172687 • Letter: C
Question
Consider an experiment that consists of counting the number of alpha particles given off in a one-second interval by one gram of radioactive material. We know from past experience that on the average 6.2 such alpha particles are given off in a two-second interval. Assuming that the number of alpha particles given off has a Poisson distribution, calculate the proability that:
a) at most 2 alpha particles are given off in a one-second interval.
b) the number of alpha particles given off in a one-second interval is greater than 2 but less than or equal to 5.
Explanation / Answer
a)
averagre for one-sec interval = 3.1
proability that at most 2 alpha particles are given off in a one-second interval = P(0)+P(1)+P(2)
= e-3.1+e-3.1*(3.1)+e-3.1*(3.1)2/2 = 0.4012
b) proability that the number of alpha particles given off in a one-second interval is greater than 2 but less than or equal to 5. = P(3)+P(4)+P(5) = e-3.1*(3.1)3/3! +e-3.1*(3.1)4/4! +e-3.1*(3.1)5/5! = 0.5045