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# Consider the following function . It is known in the field of statistics as the probability density function of the Normal Distribution or the...

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Consider the following function . It is known in the field of statistics as the probability densityfunction of the Normal Distribution or the Gaussian Distribution ._( X - C ) 2f ( x ) =`1\292 - 2 =V 2 IT __^This function corresponds to the shape of , for example , the cross- section of a sand pile underneatha hopper ( or in a sand clock ) . Plot this function and determine if it is symmetric . Find thecoordinates of the maximum ( the x - coordinate is the mean of the distribution ) and the coordinatesof the inflection points ( the x - coordinates are the standard deviation ) .*As the amount of calculation needed here is not trivial , proceed patiently and keep organized .