If the annual precipitation X in a city is a normal variate with a mean of 50 in, and a coefficient of variation (CoV) of 0.2, determine the following; a. P(40 < X ≤ 60). b. Probability that X is within 5 in. from the mean annual precipitation. c. The value of x0 such that the probability of annual precipitation exceeding x0 is only 1/4 that of not exceeding x0.

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Precipitation

Precipitation forms the basis of the water cycle on the Earth. The air is packed with water molecules in the form of moisture or water vapor. This water vapor usually rises to the atmosphere due to density differences. Precipitation represents any form of water, in liquid form or frozen form that forms in the earth's atmosphere. The water vapor up in the atmosphere condenses due to low temperature and it leads to the formation of clouds. The water vapor that forms clouds on account of condensation, is preferably known as cloud droplet. These cloud droplets when become heavy and can no longer sustain the weight of condensed water droplets, they come to the Earth in the form of rain, snow, ice pellets, and hail. Precipitation patterns, evaporation, and condensation are the three parameters that decide the global water cycle, climate change, and weather. Additionally, smoke and dust particles are equally important parameters for precipitation, as they provide the surface area for the water vapors to get condensed and to form water droplets. So they are known as condensation nuclei. The presence of other pollutants in the air also serves as condensation nuclei. Precipitation always results in the pure water supply to earth, as the salt from the seawater does not evaporate with the water.