Respuesta :
Answer:
86.47% probability that there is at least one hit in a 30-second period
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:
[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.
Mean rate of four hits per minute.
This means that [tex]\mu = 4n[/tex], in which n is the number of minutes.
What is the probability that there is at least one hit in a 30-second period
30 seconds is 0.5 minutes, so [tex]\mu = 4*0.5 = 2[/tex]
Either the site doesn't get a hit during this period, or it does. The sum of the probabilities of these events is 1. So
[tex]P(X = 0) + P(X \geq 1) = 1[/tex]
We want [tex]P(X \geq 1)[/tex]
Then
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-2}*2^{0}}{(0)!} = 0.1353[/tex]
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.1353 = 0.8647[/tex]
86.47% probability that there is at least one hit in a 30-second period
