Some notes on 12-17

a. The table tells us that approximately .8413 of the population 
     has a z-score of 1.0 or less
   The table also tells us that approximately .1587 of the population 
     has a z-score of -1.0 or less.

   .8413-.1587 = .6826

b. The table tells us that approximately .9773 of the population 
     has a z-score of 2.0 or less
   The table also tells us that approximately .0228 of the population 
     has a z-score of -2.0 or less.  

   .9773-.0228 = .9545

c. The table tells us that approximately .9987 of the population 
     has a z-score of 3.0 or less
   The table also tells us that approximately .0014 of the population
     has a z-score of -3.0 or less

   .9987-.0014 = .9973

d. [Drawing a picture may help]

   We need the middle 50%, so we start with the z-scores that give us  
   approximately 0.75 and 0.25.

   The 75th percentile somewhere between 0.67 and 0.68.  Our answer key
   uses 0.675 and we will, too

   0.675 + -0.675 = 1.35

e. [Drawing a picture may help]
   
   A high outlier has a z-score at least 1.5*1.35 above 1.65.  A
   low outlier has a z-score at least 1.5*1.35 below 1.65.

   0.675 + 1.5*1.35 = 2.7
   -0.675 - 1.5*1.35 = -2.7

   P(Z < -2.7) = .0035
   By symmetry, P(Z > 2.7) = .0035
   Total probability is .0070