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Answer:
(a) The random variable <em>X</em> is a continuous random variable.
(b) The probability density function is shown below.
(c) The probability that a 275 gallon tank gets less than 272.5 gallons or more than 273.8 gallons of water is 0.285.
Step-by-step explanation:
Let the random variable <em>X</em> be denoted as the amount of water filled by the machine in a 275 gallon tank.
(a)
The random variable <em>X</em> is a continuous random variable.
A continuous random variables assumes infinite values. That is, they assume values in a fixed interval. For example, the distance covered by a car.
A discrete random variable assumes fixed definite values. They assume whole number values. For example, number of customers visiting a bank in an hour.
The amount of water in the tank can be any value between 0 to 275 gallon.
Hence, the random variable <em>X</em> is a continuous random variable.
(b)
The probability density function of the continuous random variable <em>X</em> is given as follows:
(c)
Compute the value of P (272.5 < X < 273.8) as follows:
Thus, the probability that a 275 gallon tank gets less than 272.5 gallons or more than 273.8 gallons of water is 0.285.