Find the area under the curve and then convert it to apercentage, assuming stand

Question

Find the area under the curve and then convert it to apercentage, assuming standard normal distribution   (Basis for the range rule of thumb and the Empirical rule ): a)   Area is between z = - 2 and z = 2 (or within 2 standard deviations of the mean b)   Area is between z = - 3.5 and z = 3.5 (orwithin 3.5 standard deviations of the mean )    will rate lifesaver ! Find the area under the curve and then convert it to apercentage, assuming standard normal distribution   (Basis for the range rule of thumb and the Empirical rule ): a)   Area is between z = - 2 and z = 2 (or within 2 standard deviations of the mean b)   Area is between z = - 3.5 and z = 3.5 (orwithin 3.5 standard deviations of the mean )    will rate lifesaver !

Explanation / Answer

PART a>>>   Using tables of the normal distor using the DISTR function on a TI83plus or 84: then
choice 2.normalcdf(-2,2), we get an area of 0.9545 (rounded to 4digits). This is 95.45 % and agrees well with the 68-95-99.7 empirical rule. PART b>>>    Again, using normal Ztables or calculator, we get area of 0.9995 (rounded to 4digits). This is 99.95%.

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