Respuesta :
Answer:
(a) The probability of more than one death in a corps in a year is 0.1252.
(b) The probability of no deaths in a corps over 7 years is 0.0130.
Step-by-step explanation:
Let X = number of soldiers killed by horse kicks in 1 year.
The random variable [tex]X\sim Poisson(\lambda = 0.62)[/tex].
The probability function of a Poisson distribution is:
[tex]P(X=x)=\frac{e^{-\lambda}\lambda^{x}}{x!};\ x=0,1,2,...[/tex]
(a)
Compute the probability of more than one death in a corps in a year as follows:
P (X > 1) = 1 - P (X ≤ 1)
= 1 - P (X = 0) - P (X = 1)
[tex]=1-\frac{e^{-0.62}(0.62)^{0}}{0!}-\frac{e^{-0.62}(0.62)^{1}}{1!}\\=1-0.54335-0.33144\\=0.12521\\\approx0.1252[/tex]
Thus, the probability of more than one death in a corps in a year is 0.1252.
(b)
The average deaths over 7 year period is: [tex]\lambda=7\times0.62=4.34[/tex]
Compute the probability of no deaths in a corps over 7 years as follows:
[tex]P(X=0)=\frac{e^{-4.34}(4.34)^{0}}{0!}=0.01304\approx0.0130[/tex]
Thus, the probability of no deaths in a corps over 7 years is 0.0130.
