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wlad13 [49]
2 years ago
10

When studying radioactive material, a nuclear engineer found that over 365 days,

Mathematics
1 answer:
Gnom [1K]2 years ago
5 0

Answer:

a) The mean number of radioactive atoms that decay per day is 81.485.

b) 0% probability that on a given day, 50 radioactive atoms decayed.

Step-by-step explanation:

Poisson distribution:

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

P(X = x) = \frac{e^{-\lambda}*\lambda^{x}}{(x)!}

In which

x is the number of sucesses

e = 2.71828 is the Euler number

\lambda is the mean in the given interval.

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

29,742 atoms decayed during 365 days, which means that:

\lambda = \frac{29742}{365} = 81.485

The mean number of radioactive atoms that decay per day is 81.485.

b. Find the probability that on a given day, 50 radioactive atoms decayed.

This is P(X = 50). So

P(X = 50) = \frac{e^{-81.485}*(81.485)^{50}}{(50)!} = 0

0% probability that on a given day, 50 radioactive atoms decayed.

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