Question

When studying radioactive​ material, a nuclear engineer found that over 365​ days, 1,000,000 radioactive atoms decayed to 971,984 radioactive​ atoms, so 28,016 atoms decayed during 365 days.
a. Find the mean number of radioactive atoms that decayed in a day.
b. Find the probability that on a given​ day, 50 radioactive atoms decayed.

Answer 1

do you know that mean is

Answer 2

the mean teacher averaged their grades??

Answer 3

so you subtract 971,984 from 1 mil to get the change

Answer 4

then you divide that number by 365

Answer 5

to find the mean

Answer 6

Yes its the second half that frustrates me

Answer 7

idk about the second part

Answer 8

76.756

Answer 9

im not good at probability unless its like a bag of marbles

Answer 10

its called a poisson distribution

Answer 11

Do you know why Poisson distribution should be used here?

Answer 12

i do not, why?

Answer 13

Well, Poisson is used when:
1. Occurrences are all independent
2. We know the average number of occurrences in a time span.
3. We want to know the probability of x occurences

Answer 14

Okay

Answer 15

So are you familiar with this: \[
\Pr(X=x) = \frac{\mu^xe^{-\mu}}{x!}
\]

Answer 16

Part one lets you find \(\mu\), and part two tells you to use \(x=50\).

Answer 17

yes i have seen this before! e = 2.71828 i believe!

Answer 18

Anyway, can you plug it in then?

Answer 19

\[
\Pr(X=50) = \frac{\left(\frac{28016}{365}\right)^{50}e^{-28016/365}}{50!}
\]

Answer 20

It's going to be a very small number, because getting exactly \(50\) is not a lot

Answer 21

what is e?