Respuesta :
Answer:
a) 12.25% probability that no fatalities will occur during any given month.
b) 25.72% probability that one fatality will occur during any given month.
c) The standard deviation of x is 1.45.
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 variance is the same as the mean
One airline averages about 2.1 fatalities per month.
This means that [tex]\mu = 2.1[/tex]
(a) What is the probability that no fatalities will occur during any given month?
This is [tex]P(X = 0)[/tex]
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-2.1}*(2.1)^{0}}{(0)!} = 0.1225[/tex]
12.25% probability that no fatalities will occur during any given month.
(b) What is the probability that one fatality will occur during any given month?
This is [tex]P(X = 1)[/tex]
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 1) = \frac{e^{-2.1}*(2.1)^{1}}{(1)!} = 0.2572[/tex]
25.72% probability that one fatality will occur during any given month.
(c) Find the standard deviation of x.
The standard deviation is the square root of the variance. So
[tex]\sqrt{2.1} = 1.45[/tex]
So the standard deviation of x is 1.45.
