Graded Questions 7

The graph above represents the PDF of a uniformly distributed random variable X. As you can see, the probability density is equal for all the possible values of X (-5 to +5).

The normal distribution, aka the Gaussian distribution, was discovered by Carl Friedrich Gauss in 1809. Gauss was trying to create a probability distribution for astronomical errors. Astronomical errors are the errors that were made by astronomers while observing phenomena such as distances in space.

For example, Gauss found that an astronomer trying to estimate the distance between Earth and Uranus always makes an error. This error is normally distributed, with µ = 0 km and σ = 1,000 km.

In the light of the heavy rains and the consequent floods in Kerala, the state government decided to find out how probable these types of rainfalls are during the month of August so that they can redesign the current state infrastructure and prepare themselves for such future events.

From historical data, it was found that the average rainfall received by Kerala in the month of August was  1600 mm with a standard deviation of 400 mm. Assuming that the rainfall data follows a normal distribution,answer the following questions.

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