Question

the web site for xyz gets approximately seven visitors per mintue.suppose the number of web site visitors per minutes per minute follows a poisson probability distribution
(1)what is the mean time between visits to the web site?
(2)what is the probability no one will access the web site in a 1 minute period?
(3)what is the probability no one will access the web site in a 12 second period?

Answer 1

Answer on Question #68034 – Math – Statistics and Probability

Question

the web site for xyz gets approximately seven visitors per minute. Suppose the number of web site visitors per minute follows a Poisson probability distribution

(1) what is the mean time between visits to the web site?

(2) what is the probability no one will access the web site in a 1 minute period?

(3) what is the probability no one will access the web site in a 12 second period?

Solution

1) $\frac{1}{\mu} = \frac{1}{7}$ min. ≈ 8.6 sec.

2) $P(X = 0) = e^{-\mu} \frac{\mu^0}{0!} = e^{-7} = 0.0009$.

3) $\mu = \frac{7*12}{60} = 1.4$.

$$P(X = 0) = e^{-\mu} \frac{\mu^0}{0!} = e^{-1.4} = 0.2466.$$

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