Question

The summer monsoon rains in a country follow approximately a Normal distribution with mean 854 millimeters (mm) of rainfall and standard deviation 87 mm.
(b) "Normal rainfall" means within 20% of the long-term average, or between 683 mm and 1025 mm. In what percent of all years is the rainfall normal?

Answer 1

Answer on Question #70943 – Math – Statistics and Probability

Question

The summer monsoon rains in a country follow approximately a Normal distribution with mean 854 millimeters (mm) of rainfall and standard deviation 87 mm.

(b) "Normal rainfall" means within 20% of the long-term average, or between 683 mm and 1025 mm. In what percent of all years is the rainfall normal?

Solution

$$\begin{array}{l} P(683 < X < 1025) = P\left(\frac{683 - 854}{87} < Z < \frac{1025 - 854}{87}\right) = \\ = P(-1.97 < Z < 1.97) = P(Z < 1.97) - P(Z < -1.97) = 0.9512, \text{ that is,} \\ 95.12\%. \end{array}$$

Answer: 95.12%.

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