A local gas station waits 4 days to receive a delivery of regular gasoline to re

Question

A local gas station waits 4 days to receive a delivery of regular gasoline to replenish its inventory. The wait period to receive inventory is known   as the lead time. The demand during the lead-time period for regular gasoline, as measured in gallons, follows the normal distribution with a mean of 930 gallons and standard deviation of 140 gallons.(25 point)

a) Which probability distribution will be for use of gasoline?

1) Discrete Probability Distribution

2) Continuous Probability Distribution

b) Which probability distribution we can use for the level of gasoline?

1) Binomial Probability Distribution

2) Normal Probability Distribution

3) Exponential Probability Distribution

4) Uniform Probability Distribution

c) What is the probability that during the next lead time, the demand for regular gasoline will be less than 800 gallons?

d) Determine the reorder point that will ensure the station a 90% probability that will have enough inventory of regular gasoline until        the next order arrives.

Explanation / Answer

a) Which probability distribution will be for use of gasoline?

2) Continuous Probability Distribution is the answer .

b) Which probability distribution we can use for the level of gasoline?

2) Normal Probability Distribution is the answer

(c) Here if X is the demand for regular gasoline.

Pr(X < 800 gallons) = NORM (X < 800 ; 930 ; 140)

Z = (800 - 930)/ 140 = -0.9286

Pr(X < 800 gallons) = NORM (X < 800 ; 930 ; 140) = Pr(Z < -0.9286) = 0.17655

(d) Determine the reorder point that will ensure the station a 90% probability that will have enough inventory of regular gasoline until        the next order arrives?

Answer :

Let say that point is X0 gallon.

Pr(X < Xo  ) = 0.90

Here Z value for p - value quals to 0.90 is 1.645

Pr(X < Xo  ) = NORM(X < Xo ; 930 ; 140) = 1.645

( X0 - 930)/140 = 1.645

X0 = 930 + 140 * 1.645 = 1160.3 gallons

so it must be ordered when there is 1160.3 gallons left

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