Question

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 1

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