Question

You are trying to understand the error surrounding the precipitation estimate that you obtained from one of your rain gages. You have determined that for this gage you have a standard error of 30%. For a precipitation event of 5 inches, what is the probability that the actual event is less than 6.5 inches (please assume a normal distribution) (please also provide the response without a percent sign and in the following numerical format: 00.00)

Answer 1

Answer:

The probability that the actual event is less than 6.5 inches is 0.9999.

Step-by-step explanation:

We are given that you have determined that for this gage you have a standard error of 30%.

For a precipitation event of 5 inches, we have to find the probability that the actual event is less than 6.5 inches.

The z-score probability distribution for the normal distribution is given by;

                             Z = $\frac{X-\mu}{\frac{\sigma}{\sqrt{n} } }$  ~ N(0,1)

where, $\mu$ = mean precipitation event = 5 inches

           standard error = $\frac{\sigma}{\sqrt{n} }$ = 0.30

Now, the probability that the actual event is less than 6.5 inches is given by = P(X < 6.5 inches)

      P(X < 6.5 inches) = P( $\frac{X-\mu}{\frac{\sigma}{\sqrt{n} } }$ < $\frac{6.5-5}{0.30}$ ) = P(Z < 5) = 0.9999

The above probability is calculated by looking at the value of x = 5 but in the z table the last value of x is given as 4.40 so we take the area of that value only which has an area of 0.9999.