when consider a normal distribution with mean =0 and standard deviation=1 and z is the z value in standard notation.
1) percent of data is within 1 standard deviation of the mean"(P_1),"
"P_1=P(-1<z<1)=2*P(0<z<1)"
(using calculator or table probability can be calculated)
"P_1=2*0.34134=0.68268=\\bold{68.268\\%}"
2) percent of data is within the mean and 2 standard deviations above the mean"(P_2)" ,
"P_2=P(0<z<2) \\\\"
(using calculator or table probability can be calculated)
"P_2=0.47725=\\bold{47.725\\%}"
3) percent of data is more than 2 standard deviations above the mean "(P_3),"
"P_3=P(z>2)\\\\"
(using calculator or table probability can be calculated)
"P_3=0.02275=\\bold{2.275\\%}"
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