Question

A service station has a pump that distributes diesel fuel to trucks. The station owner estimates that on average every two hours, 3 trucks stop to get diesel fuel. Assume that the arrival of diesel fuel users are Poisson distributed.

a) What is the expected average number of trucks over a one-hour period? Give the answer correct to two digits after the decimal point  

Enter all probabilities as a percent, correct to two digits after the decimal point, without the percent symbol.

b) What is the probability that 2 trucks arrive to get diesel fuel during a two-hour period?  

c) What is the probability that 2 trucks arrive to get diesel fuel during a one-hour period?  

d) What is the probability that 3 or more trucks arrive to get diesel fuel during a two-hour period?  

e) What is the probability that less than 2 trucks arrive to get diesel fuel during a two-hour period?

Answer 1

a_)

expected average number of trucks over a one-hour period =3/2 =1.50

b) probability that 2 trucks arrive to get diesel fuel during a two-hour period =P(X=2)=e^-33²/2! =0.2240

~ 22.40%

c)

probability that 2 trucks arrive to get diesel fuel during a one-hour period =P(X=2)=e^-1.51.5²/2! =0.2510 ~ 25.10 %

d)

probability that 3 or more trucks arrive to get diesel fuel during a two-hour period

P(X>=3)=1-P(X<=2)=

1-∑x=02 e-3*3x/x!=

0.5768 ~ 57.68 %

e)

probability that less than 2 trucks arrive to get diesel fuel during a two-hour period:

P(X<=1)=

∑x=0x   {e-λ*λx/x!}=

0.1991 ~ 19.91 %