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 97.5%; that is, he wants to have a 97.5% chance that he does not run out of gas on any day and only wants a 2.5% 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: Beween (mean - 2 sigmas) and (mean + 2 sigmas) under a normal distribution, approximately 95% probability is covered, leaving 2.5% on each of the two tails. Therefore, the 97.5th percentile under a normal distribution is approximately at mean + 2 sigmas.)

Group of answer choices

A:600 gallons

B:1400 gallons

C:1000 gallons

D:800 gallons

Answer 1

From the z table, we can find out that, z score for 95% probability = 1.96

Also, z =

Therefore x =

Therefore,

Amount of gas should Bilbo hold by refilling his tank at the beginning of the day =

Amount of gas should Bilbo hold by refilling his tank at the beginning of the day = Mean + z*Standard deviation

Amount of gas should Bilbo hold by refilling his tank at the beginning of the day = 1000 + 1.96*200 = 1000+392 = 1392.

For a 95% probability of not running out on gas, we need 1392 gallons of gas every day. To reach 97.5% probability of not running out of gas we'll need a higher amount of gas.

There's only one option higher than 1392 which is 1400.

Hence Option B:1400 is the correct answer.