Question

1. About what percent of data is within 1 standard deviation of the mean?


2. About what percent of data is within the mean and 2 standard deviations above the mean?


3. About what percent of data is more than 2 standard deviations above the mean?

Answer 1

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)

$P_3=0.02275=\bold{2.275\%}$