When studying radioactive material, a nuclear engineer found that over 365 days, 1,000,000 radioactive atoms decayed to 973 comma 903 radioactive atoms, so 26 comma 097 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: 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