Question

The demand for water in a certain town (in million gallons) follows an exponential distribution with (lambda)=1/8

If the capacity of the water resources is of 10 million gallons, what is the probability that in any given day, the supply will not be enough?

In the next 10 days, what is the probability that we would have a water shortage in exactly two days?

If an inspector arrives, and every day checks if there is a water shortage, how many days on average will he have to maintain his inspection if he stops when he finds 2 days with water shortages?

What is the probability that the water consumption total in a week is between 56 and 70 million gallons?

What is the probability that the water consumption total in a month is between 200 and 240 million gallons?

Answer 1

for exponential distribution

P = ?e^-?x

Where:
   ?: The rate parameter of the distribution, = 1/µ (Mean)
   P: Exponential probability density function
   x: The independent random variable?

there will be a shortage if the water consumption (x) exceeds 10

the probability that in any given day, the supply will not be enough

We need to compute Therefore, the following is obtained:

the probability that the water consumption total in a week is between 56 and 70 million gallons:

for a week

the probability that the water consumption total in a month is between 200 and 240 million gallons

for a month