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Sagot :
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:
[tex]P(X = x) = \frac{e^{-\lambda}*\lambda^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\lambda[/tex] 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:
[tex]\lambda = \frac{29742}{365} = 81.485[/tex]
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
[tex]P(X = 50) = \frac{e^{-81.485}*(81.485)^{50}}{(50)!} = 0[/tex]
0% probability that on a given day, 50 radioactive atoms decayed.
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