Respuesta :
Answer:
11.18% probability that the city's weather station records exactly 4 snowstorms with at least 12 inches of total snow accumulation for one randomly selected year in the 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 time interval.
78 snowstorms with at least 12 inches of total snow accumulation.
This means that [tex]\mu = \frac{78}{12} = 6.5[/tex]
Find the probability that the city's weather station records exactly 4 snowstorms with at least 12 inches of total snow accumulation for one randomly selected year in the period.
This is P(X = 4). So
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 4) = \frac{e^{-6.5}*(6.5)^{4}}{(4)!} = 0.1118[/tex]
11.18% probability that the city's weather station records exactly 4 snowstorms with at least 12 inches of total snow accumulation for one randomly selected year in the period.
