The demand for gasoline at a local service station is normally distributed with

Question

The demand for gasoline at a local service station is normally distributed with a mean of 27,009 gallons per day and a standard deviation of 4,530 gallons per day.

a. Find the probability that the demand for gasoline exceeds 22,000 gallons for a given day.
b. Find the probability that the demand for gasoline falls between 20,000 and 23,000 gallons for a given day.
c. How many gallons of gasoline should be on hand at the beginning of each day so that we can meet the demand 90% of the time (i.e., the station stands a 10% chance of running out of gasoline for that day)

Explanation / Answer

The demand for gasoline at a local service station is normally distributed with a mean of 27,009 gallons per day and a standard deviation of 4,530 gallons per day.

a. Find the probability that the demand for gasoline exceeds 22,000 gallons for a given day.

Z value for 22000, z=(22000-27009)/4530 = -1.15

P( x >22000) =P(z > -1.15) = 0.8749

b. Find the probability that the demand for gasoline falls between 20,000 and 23,000 gallons for a given day.
Z value for 20000, z=(20000-27009)/4530 = -1.61

Z value for 23000, z=(23000-27009)/4530 = -0.62

P( 20000 <x<23000) = P( -1.61 <z <-0.62)

P( z < -0.62) – P( z < -1.61)

= 0.1251 - 0.0537

=0.0714

c. How many gallons of gasoline should be on hand at the beginning of each day so that we can meet the demand 90% of the time (i.e., the station stands a 10% chance of running out of gasoline for that day)

z value for bottom 90% = 1.282

x value = 27009 +1.282*4530 = 32816.46

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