Question 411240
  <pre><font size = 3 color = "indigo"><b>
Hi
*Note: {{{z = blue(x - mu)/blue(sigma)}}} 
On an exam with a mean of M=82, you obtain a score of X=86  
a. Would you prefer a standard deviation of s=2 or s=10?  s = 2
   z = 4/2 = 2  OR z= 4/10 = .4
b. If your score were X=78, would you prefer s=2 or s=10?  s = 10
  z =  -4/2 = -2  OR z = -4/10 = -.4
c. If one scores below the mean, one wants the SD to be larger. 
If one scores above the mean , one would wish the SD to be smaller. 
That is: it will reflect a better position as to placement on the curve.
{{{drawing(300,300,-5,5,-1,1,blue(line(2,5,2,-5)),blue(line(-.4,5,-.4,-5)), grid(1),graph( 300, 300,-5,5,-1,1,(1/sqrt(2*pi))*3^((-x^2/2)))) }}}