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kipiarov [429]
3 years ago
11

Cargo ships arrive at a loading dock at a rate of 2 per day. The dock has the capability of handling 3 arrivals per day. How man

y days per month (assume 30 days in a month) would you expect the dock being unable to handle all arriving ships? (Hint: first find the probability that more than 3 ships arrive and then use that probability to find the expected number of days in a month too many ships arrive.)
Mathematics
1 answer:
Vsevolod [243]3 years ago
6 0

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)]

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}]

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

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