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Sagot :
Answer:
0.2209 = 22.09% probability that in a randomly selected office hour, the number of student arrivals is 3.
Step-by-step explanation:
We have the mean during an interval, so the Poisson distribution is used.
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^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
A statistics professor finds that when she schedules an office hour for student help, an average of 3.3 students arrive.
This means that [tex]\mu = 3.3[/tex]
Find the probability that in a randomly selected office hour, the number of student arrivals is 3.
This is P(X = 3). So
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 3) = \frac{e^{-3.3}*3.3^{3}}{(3)!} = 0.2209[/tex]
0.2209 = 22.09% probability that in a randomly selected office hour, the number of student arrivals is 3.
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