Answer:
0.827
Step-by-step explanation:
Data provided in the question:
Probability of breakdown, p = once in 3 weeks i.e [tex]\frac{1}{3}[/tex]
number of weeks n = 21
now,
mean, λ = np
= [tex]\frac{1}{3}\times21[/tex]
= 7
P(X > 4) = 1 - ( P(X ≤ 4))
using Poisson distribution
P(X = x) = [tex]\frac{e^{-\lambda}\lambda^x}{x!}[/tex]
Thus,
P(X = 0) = [tex]\frac{e^{-7}7^0}{0!}[/tex]
= 0.00091
P(X = 1) = [tex]\frac{e^{-7}7^1}{1!}[/tex]
= 0.00638
P(X = 2) = [tex]\frac{e^{-7}7^2}{2!}[/tex]
= 0.02234
P(X = 3) = [tex]\frac{e^{-7}7^3}{3!}[/tex]
= 0.05213
P(X = 4) = [tex]\frac{e^{-7}7^4}{4!}[/tex]
= 0.09123
Thus,
P(X ≤ 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)
= 0.00091 + 0.00638 + 0.02234 + 0.05213 + 0.09123
= 0.17299
Therefore,
P(X > 4) = 1 - 0.17299
= 0.827
