Question

# Speedway LLC is an American convenience store and gas station chain headquartered in Enon, Ohio, with...

Speedway LLC is an American convenience store and gas station chain headquartered in Enon, Ohio, with locations primarily in the Midwest and the East Coast regions of the United States. The amount of regular unleaded gasoline sold at the Speedway gas station in Macedonia, OH is distributed as a uniform random variable between 1,200 and 3,450 gallons each day.

What is the probability that this Speedway gas station will sell more than 2,000 gallons of regular unleaded gasoline today?

What is the probability that this Speedway gas station will sell between 2,500 and 2,800 gallons of regular unleaded gasoline today?

What is the standard deviation of this probability distribution?

Solution :

Given that,

a = 1200

b = 3450

a) P(x > c) = (b - c) / (b - a)

P(x > 2000) = (3450 - 2000) / (3450 - 1200)

P(x > 2000) = 0.6444

b) P(c < x < d) = (d - c) / (b - a)

P(2500 < x < 2800) = (2800 - 2500) / (3450 - 1200)

P(2500 < x < 2800) = 0.1333

c) standard deviation =  (b - a) / 12

standard deviation =  (3450 - 1200) / 12

standard deviation = 0.83

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