Question 1173830
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Hi,

Normal Distribution:
µ = 496  ,   σ = 114      {{{z = blue(x - mu)/blue(sigma)}}}
{{{X[Billy] = 334 }}}
 z = (334-496)/114  = -1.4 (nearest tenth)
{{{X[Xito] = 375 }}}
 z = (375 - 496)/114 = -1.1
Which student scored better based on their z score, Billy or <u>Xito</u>
  -1.4 < -1.1   Billy z-score further away from the mean.
Wish You the Best in your Studies.
{{{drawing(400,200,-5,5,-.5,1.5, graph(400,200,-5,5,-.5,1.5, exp(-x^2/2)), green(line(1,0,1,exp(-1^2/2)),line(-1,0,-1,exp(-1^2/2))),green(line(2,0,2,exp(-2^2/2)),line(-2,0,-2,exp(-2^2/2))),green(line(3,0,3,exp(-3^2/2)),line(-3,0,-3,exp(-3^2/2))),green(line( 0,0, 0,exp(0^2/2))),locate(4.8,-.01,z),locate(4.8,.2,z))}}}
For the normal distribution: 
one  standard deviation from the mean accounts for about 68.2% of the set 
two standard deviations from the mean account for about 95.4%
and three standard deviations from the mean account for about 99.7%.
Important to Understand z -values as they relate to the Standard Normal curve: