Question

Bilbo owns a gas station. He refills his gas tank once a day early in the morning. Historical data show that daily demand at his gas station is relatively stable and has mean = 1000 gallons and standard deviation = 200 gallons. His gas tank has a capacity of holding up-to 3000 gallons of gasoline so that is not an issue. Holding gasoline will occupy financial resources, though, and therefore Bilbo does not want to hold too much gasoline in his tank. He wants to maintain a service level of 90%; that is, he wants to have a 90% chance that he does not run out of gas on any day and only wants a 10% chance to face angry customers by running out inventory. How much gas should Bilbo hold by refilling his tank at the begining of the day? (Hint: use the NORMINV or NORMSINV function on Excel to find out where the 90th percentile is under the given normal distribution.)

Group of answer choices

A: =NORMINV(0.9,200,1000) = 1481.55 gallons

B: =1000+200*NORMSINV(0.9) = 1256.31 gallons

C: =1000+200*0.9 = 1180 gallons

D: =1000*NORMSINV(0.9) = 1281.55 gallons

Answer 1

Theory:

Norminv returns the inverse of normal cumulative distribution for a specified mean and standard deviation. Has 3 parameters of probability, mean, and standard deviation.

Normsinv returns a standard normal cumulative distribution(Mean = 0 & standard deviation of 1). Has only one parameter of probability.

Option evaluation:

A: =NORMINV(0.9,200,1000) = 1481.55 gallons

The formulation is correct but the final answer is incorrect. Hence this option is incorrect.

B:=1000+200*NORMSINV(0.9) = 1256.31 gallons

Both formulation and the final answer are correct. This is the correct option.

C:  =1000+200*0.9 = 1180 gallons

Doesn't utilize any excel function to ensure normal distribution. Both formulation and final answer incorrect. Hence this option is incorrect.

D. =1000*NORMSINV(0.9) = 1281.55 gallons

Doesn't utilize standard deviation value hence both formulation and final answer incorrect. Hence this option is incorrect.