When studying radioactive material, a nuclear engineer found that over 365 days, 1,000,000 radioactive atoms decayed to 972 comma 737 radioactive atoms, so 27 comma 263 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, 51 radioactive atoms decayed.

a) 74.69

b) 0.08% probability that on a given day, 51 radioactive atoms decayed.

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

In which

x is the number of sucesses

e = 2.71828 is the Euler number

is the mean in the given time interval.

a. Find the mean number of radioactive atoms that decayed in a day.

27,263 atoms in 365 days. The mean is

b. Find the probability that on a given day, 51 radioactive atoms decayed.

This is P(X = 51).

0.08% probability that on a given day, 51 radioactive atoms decayed.

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step-by-step explanation: