Suppose that the daily demand for gas (in thousands of litres) at a certain gas

Question

Suppose that the daily demand for gas (in thousands of litres) at a certain gas station is an exponential random variable with mean equal to 2. Every morning the station's tank is filled to rapacity. What is the probability that they.sell more than 2000 litres in a given day? Find the median daily sales for the gas station in thousands of litres. That Li, the value in such that the gas station sells less than m thousand litres in a day 50% of the time and soils more than m thousand litres in a day the other 50% of the time. What size must the tank be to ensure that the probability of running out of gas on any given day is only 1%.

Explanation / Answer

a)

The mean of the distirbution is

mean = u =    2      

The right tailed area in an exponential distribution is          
          
P(x>x1) = e^(-x1/u)          
          
As          
          
x1 = critical value =    2      
          
          
Then          
          
Area =    0.367879441   [ANSWER]

***************************

b)

For exponential distributions,

Median = -u ln(0.5)

Then as u = 2,

Median = -2*ln(0.5) = 1.386294361 [ANSWER]

***************************

c)

The right tailed area in an exponential distribution of mean u = 2 is
          
P(x>x1) = e^(-x1/2)          

Hence,

e^(-x1/2) = 0.01

Thus,

x1 = -2*ln(0.01) = 9.210340372 [ANSWER]

          
  

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.