Question

In a 40-year period, a city's official weather station recorded 78 snowstorms with at least 12 inches of total snow accumulation. Assume that this pattern follows a Poisson distribution. 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. Use Excel to find the probability.

Answer 1

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:

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

In which

x is the number of sucesses

e = 2.71828 is the Euler number

$\mu$ is the mean in the given time interval.

78 snowstorms with at least 12 inches of total snow accumulation.

This means that $\mu = \frac{78}{12} = 6.5$

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

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

$P(X = 4) = \frac{e^{-6.5}*(6.5)^{4}}{(4)!} = 0.1118$

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.