The demand of gasoline in a gas station is distributed unifo

The demand of gasoline in a gas station is distributed uniformly between 2000 and 4000 gallons a day.

a.What is the probability density function?

b.What is the mean number of gallons sold every day?

c.What is the probability of stock out if the station has 3500 gallons at the start of the day?

d.How many gallons are needed to ensure 90% of the time the station won’t run out of gasoline?

Solution

A)

f(x) = 1/(4000-2000), 2000<x<4000
0 otherwise

or

f(x) = 0.0005 , 2000<x<4000
0 otherwise [ANSWER]

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b)

mean = (a+b)/2 = (4000+2000)/2 = 3000 [ANSWER]

c)

P(X>3500) = 0.0005*(4000-3500) = 0.25 [ANSWER]

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d)

If P(X<x) = 0.90, then

(x-2000)*0.0005 = 0.90

x-2000 = 1800

x = 3800 [ANSWER]

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