Question

The National Weather Service issues precipitation forecasts thatindicate. Thelikelihood of measurable precipitation (Ú .01 inch) at a specific point(the official rain gauge) during agiven time period. Suppose that if a measurable amountof rain falls during the next 24 hours, a river will reachthe flood stage, and a business will incur damages of $300,000. The National Weather Service has indicated that there isa 30% chance of a measurable amount of rain during thenext 24 hours.

a.Construct the probability distribution that describes thepotential flood damages.

b.Find the firm’s expected loss due to flood damage.

Short answer

a. There are potential flood damages following Bernoulli distribution.

b. The expected loss due to damage$\$2700000$ .

Step-by-step solution

Given information

The likelihood of measurable precipitation is$0.01$ inches. The business will incur damages of $300000$. The weather service would be indicated that there is a $30\%$chance of a measurable amount of rain.

(a) Construct the probability distribution

Constructing the distribution that describes the potential flood damages is:

This flood damage follows Bernoulli distribution. Because there are two possible casesof rain and not rain, in this case, the distribution will follow the Bernoulli distribution.

We must determine the probability distribution of possible rain damage.

Let x represent the flood damage.

Given that if a flood occurs, the firm will suffer a $300,000 loss.

If the flood does not occur, the firm is not harmed.

National weather agencies predicted a 30% probability of rain.

The probability distribution of X is thus

(b) Find the expected loss due to flood damage

The expected loss is given by

$$\begin{gathered} 3000000\times \frac{30}{100} \\ =90,000 \end{gathered}$$

So, there are expected loss of $$90,000$