Respuesta :
Answer:
The average number of days that will pass between measurable rain is 7.5.
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 time interval.
The expected period between the event happening is [tex]\frac{1}{\mu}[/tex]
During the dry month of August, one U.S. city has measurable rain on average only 4 days per month. Assume all months have 30 days.
This means that
[tex]\mu = \frac{4}{30}[/tex]
(a) If the arrival of rainy days is Poisson distributed in this city during the month of August, what is the average number of days that will pass between measurable rain? *
[tex]\frac{1}{\frac{4}{30}} = \frac{30}{4} = 7.5[/tex]
The average number of days that will pass between measurable rain is 7.5.
