Answer: A) 71.498 ; b) 0.00152
Step-by-step explanation:
Given the following :
Number of atoms that decayed during 365 days period = 26,097
Number of days = 365
Mean number of radioactive atoms that decayed in a day:
Mean = number of decayed atoms / number rof days
Mean = 26,097 / 365
Mean = 71.498 atoms per day
B.) probability that 50 radioactive atoms decayed in a given day:
Using the poisson distribution formula :
P(x =x) = (m^x * e^-m) ÷ x!
Where m = mean
Mean (m) = 71.498
P(x = 50) = (71.498^50 * e^-71.498) / 50!
P(x = 50) = (71.498^50 * 2.7182818^-71.498) / 50!
= 4.60795E61 / 50!
= 0.0015150
