Final answer:
In this question, we calculate the probability of different daily sales of gasoline at a service station that has a uniform distribution. We find the probability of sales falling between specific ranges and the probability of selling at least a certain amount. We also explain why the probability of selling exactly a specific amount is zero.
Step-by-step explanation:
In this question, we are given that the amount of gasoline sold daily at a service station is uniformly distributed with a minimum of 2,000 gallons and a maximum of 5,000 gallons.
(a) To find the probability that daily sales will fall between 2,500 and 3,000 gallons, we need to calculate the area under the probability distribution curve between these two values. Since the distribution is uniform, the probability density is constant within the range. The probability can be calculated as:
P(2,500 < x < 3,000) = (3,000 - 2,500) / (5,000 - 2,000) = 0.1667
(b) To find the probability that the service station will sell at least 4,000 gallons, we need to calculate the area under the probability distribution curve from 4,000 gallons to the maximum value of 5,000 gallons. Again, since the distribution is uniform, the probability density is constant within this range. The probability can be calculated as:
P(x >= 4,000) = (5,000 - 4,000) / (5,000 - 2,000) = 0.3333
(c) To find the probability that the station will sell exactly 2,500 gallons, we need to calculate the probability of a single point in the distribution. Since the distribution is continuous, the probability of a single point is zero. Therefore, the probability of selling exactly 2,500 gallons is zero.