Answer:
4 days
Step-by-step explanation:
We need to use the probability functions of each of the intervals to know the Probability number and then use it in the expected value.
P(x>3 cargo ships) = 1-P(x<=3)
P(x>3) = 1-P(x<=3)
P(x>3) = 1-[P(x=0)+P(x=1)+P(x=2)+P(x=3)]
[tex]P(x>3) = 1 - [\frac{e^{-2}2^0}{01}+\frac{e^{-2}2^1}{11}+\frac{e^{-2}2^2}{21}+\frac{e^{-3}2^3}{31}][/tex]
P(x>3) = 1- [0.1353(1+2+2+1.33)]
P(x>3) = 1-0.856
P(x>3) = 0.1431
Als n=30, expected number is
E(x) =30*P(x>3)
E(x) = 30*0.1431
E(x) = 4.293
I expect 4.293 or 4 days per month the block being unable to hanlde all arriving ships
