<PRE><B>Question 1019931</B>
Given that z is a standard normal random variable, 
find z for each situation.
&lt;pre&gt;
Instead of doing your problem for you, I&#39;ve drawn the normal
curve graphs, and shaded the area mentioned.  All you have to
do is look on the z-axis of each graph and find which value on
your list of answers is closest to the z-score along that z-axis 
where the shading stops or starts, depending on whether the area 
is to the left or to the right. Here are the shaded graphs:

a) The area to the left of z is 0.9750. 

{{{drawing(400,200,-5,5,-.5,1.5,locate(4.8,-.01,z),locate(4.8,.2,z),
 graph(400,200,-5,5,-.5,1.5, exp(-x^2/2)),
line(-5,0,-5,0.37266532*10^(-5)),line(-4.9,0,-4.9,0.6113568*10^(-5)),line(-4.8,0,-4.8,0.99295043*10^(-5)),line(-4.7,0,-4.7,0.15966784*10^(-4)),line(-4.6,0,-4.6,0.25419347*10^(-4)),line(-4.5,0,-4.5,0.40065297*10^(-4)),line(-4.4,0,-4.4,0.62521504*10^(-4)),line(-4.3,0,-4.3,0.96593414*10^(-4)),line(-4.2,0,-4.2,0.14774836*10^(-3)),line(-4.1,0,-4.1,0.22374579*10^(-3)),line(-4.0,0,-4.0,0.33546263*10^(-3)),line(-3.9,0,-3.9,0.49795542*10^(-3)),line(-3.8,0,-3.8,0.73180242*10^(-3)),line(-3.7,0,-3.7,0.10647662*10^(-2)),line(-3.6,0,-3.6,0.15338107*10^(-2)),line(-3.5,0,-3.5,0.21874911*10^(-2)),line(-3.4,0,-3.4,0.30887154*10^(-2)),line(-3.3,0,-3.3,0.431784*10^(-2)),line(-3.2,0,-3.2,0.59760229*10^(-2)),line(-3.1,0,-3.1,0.8188701*10^(-2)),line(-3.0,0,-3.0,0.11108997*10^(-1)),line(-2.9,0,-2.9,0.14920786*10^(-1)),line(-2.8,0,-2.8,0.19841095*10^(-1)),line(-2.7,0,-2.7,0.2612141*10^(-1)),line(-2.6,0,-2.6,0.34047455*10^(-1)),line(-2.5,0,-2.5,0.43936934*10^(-1)),line(-2.4,0,-2.4,0.56134763*10^(-1)),line(-2.3,0,-2.3,0.71005354*10^(-1)),line(-2.2,0,-2.2,0.88921617*10^(-1)),line(-2.1,0,-2.1,0.11025053),line(-2.0,0,-2.0,0.13533528),line(-1.9,0,-1.9,0.16447446),line(-1.8,0,-1.8,0.1978987),line(-1.7,0,-1.7,0.23574608),line(-1.6,0,-1.6,0.2780373),line(-1.5,0,-1.5,0.32465247),line(-1.4,0,-1.4,0.3753111),line(-1.3,0,-1.3,0.42955736),line(-1.2,0,-1.2,0.48675226),line(-1.1,0,-1.1,0.54607443),line(-1.0,0,-1.0,0.60653066),line(-0.9,0,-0.9,0.66697681),line(-0.8,0,-0.8,0.72614904),line(-0.7,0,-0.7,0.78270454),line(-0.6,0,-0.6,0.83527021),line(-0.5,0,-0.5,0.8824969),line(-0.4,0,-0.4,0.92311635),line(-0.3,0,-0.3,0.95599748),line(-0.2,0,-0.2,0.98019867),line(-0.1,0,-0.1,0.99501248),line(-0.10269563e-14,0,-0.10269563e-14,1.0),line(0.1,0,0.1,0.99501248),line(0.2,0,0.2,0.98019867),line(0.3,0,0.3,0.95599748),line(0.4,0,0.4,0.92311635),line(0.5,0,0.5,0.8824969),line(0.6,0,0.6,0.83527021),line(0.7,0,0.7,0.78270454),line(0.8,0,0.8,0.72614904),line(0.9,0,0.9,0.66697681),line(1.0,0,1.0,0.60653066),line(1.1,0,1.1,0.54607443),line(1.2,0,1.2,0.48675226),line(1.3,0,1.3,0.42955736),line(1.4,0,1.4,0.3753111),line(1.5,0,1.5,0.32465247),line(1.6,0,1.6,0.2780373),line(1.7,0,1.7,0.23574608),line(1.8,0,1.8,0.1978987),line(1.9,0,1.9,0.16447446),locate(20,20,1))}}}

b) The area between 0 and z is 0.4750.

{{{drawing(400,200,-5,5,-.5,1.5, locate(4.8,-.01,z),locate(4.8,.2,z),
graph(400,200,-5,5,-.5,1.5, exp(-x^2/2)),
line(0,0,0,1.0),line(0.1,0,0.1,0.99501248),line(0.2,0,0.2,0.98019867),line(0.3,0,0.3,0.95599748),line(0.4,0,0.4,0.92311635),line(0.5,0,0.5,0.8824969),line(0.6,0,0.6,0.83527021),line(0.7,0,0.7,0.78270454),line(0.8,0,0.8,0.72614904),line(0.9,0,0.9,0.66697681),line(1.0,0,1.0,0.60653066),line(1.1,0,1.1,0.54607443),line(1.2,0,1.2,0.48675226),line(1.3,0,1.3,0.42955736),line(1.4,0,1.4,0.3753111),line(1.5,0,1.5,0.32465247),line(1.6,0,1.6,0.2780373),line(1.7,0,1.7,0.23574608),line(1.8,0,1.8,0.1978987),line(1.9,0,1.9,0.16447446),locate(20,20,1))}}}

c) The area to the left of z is 0.7291.

{{{drawing(400,200,-5,5,-.5,1.5, locate(4.8,-.01,z),locate(4.8,.2,z),
graph(400,200,-5,5,-.5,1.5, exp(-x^2/2)),
line(-5,0,-5,0.37266532*10^(-5)),line(-4.9,0,-4.9,0.6113568*10^(-5)),line(-4.8,0,-4.8,0.99295043*10^(-5)),line(-4.7,0,-4.7,0.15966784*10^(-4)),line(-4.6,0,-4.6,0.25419347*10^(-4)),line(-4.5,0,-4.5,0.40065297*10^(-4)),line(-4.4,0,-4.4,0.62521504*10^(-4)),line(-4.3,0,-4.3,0.96593414*10^(-4)),line(-4.2,0,-4.2,0.14774836*10^(-3)),line(-4.1,0,-4.1,0.22374579*10^(-3)),line(-4.0,0,-4.0,0.33546263*10^(-3)),line(-3.9,0,-3.9,0.49795542*10^(-3)),line(-3.8,0,-3.8,0.73180242*10^(-3)),line(-3.7,0,-3.7,0.10647662*10^(-2)),line(-3.6,0,-3.6,0.15338107*10^(-2)),line(-3.5,0,-3.5,0.21874911*10^(-2)),line(-3.4,0,-3.4,0.30887154*10^(-2)),line(-3.3,0,-3.3,0.431784*10^(-2)),line(-3.2,0,-3.2,0.59760229*10^(-2)),line(-3.1,0,-3.1,0.8188701*10^(-2)),line(-3.0,0,-3.0,0.11108997*10^(-1)),line(-2.9,0,-2.9,0.14920786*10^(-1)),line(-2.8,0,-2.8,0.19841095*10^(-1)),line(-2.7,0,-2.7,0.2612141*10^(-1)),line(-2.6,0,-2.6,0.34047455*10^(-1)),line(-2.5,0,-2.5,0.43936934*10^(-1)),line(-2.4,0,-2.4,0.56134763*10^(-1)),line(-2.3,0,-2.3,0.71005354*10^(-1)),line(-2.2,0,-2.2,0.88921617*10^(-1)),line(-2.1,0,-2.1,0.11025053),line(-2.0,0,-2.0,0.13533528),line(-1.9,0,-1.9,0.16447446),line(-1.8,0,-1.8,0.1978987),line(-1.7,0,-1.7,0.23574608),line(-1.6,0,-1.6,0.2780373),line(-1.5,0,-1.5,0.32465247),line(-1.4,0,-1.4,0.3753111),line(-1.3,0,-1.3,0.42955736),line(-1.2,0,-1.2,0.48675226),line(-1.1,0,-1.1,0.54607443),line(-1.0,0,-1.0,0.60653066),line(-0.9,0,-0.9,0.66697681),line(-0.8,0,-0.8,0.72614904),line(-0.7,0,-0.7,0.78270454),line(-0.6,0,-0.6,0.83527021),line(-0.5,0,-0.5,0.8824969),line(-0.4,0,-0.4,0.92311635),line(-0.3,0,-0.3,0.95599748),line(-0.2,0,-0.2,0.98019867),line(-0.1,0,-0.1,0.99501248),line(-0.10269563e-14,0,-0.10269563e-14,1.0),line(0.1,0,0.1,0.99501248),line(0.2,0,0.2,0.98019867),line(0.3,0,0.3,0.95599748),line(0.4,0,0.4,0.92311635),line(0.5,0,0.5,0.8824969),line(0.6,0,0.6,0.83527021),line(0.7,0,0.7,0.78270454),locate(20,20,1))}}}

d) The area to the right of z is 0.1314. 

{{{drawing(400,200,-5,5,-.5,1.5, locate(4.8,-.01,z),locate(4.8,.2,z),
graph(400,200,-5,5,-.5,1.5, exp(-x^2/2)),
line(1.11979765,0,1.11979765,0.53420619),line(1.21979765,0,1.21979765,0.47523153),line(1.31979765,0,1.31979765,0.41856088),line(1.41979765,0,1.41979765,0.36498001),line(1.51979765,0,1.51979765,0.31509142),line(1.61979765,0,1.61979765,0.26931537),line(1.71979765,0,1.71979765,0.22789917),line(1.81979765,0,1.81979765,0.19093318),line(1.91979765,0,1.91979765,0.15837154),line(2.01979765,0,2.01979765,0.13005585),line(2.11979765,0,2.11979765,0.1057401),line(2.21979765,0,2.21979765,0.08511510),line(2.31979765,0,2.31979765,0.67831366*10^(-1)),line(2.41979765,0,2.41979765,0.5351944*10^(-1)),line(2.51979765,0,2.51979765,0.41807058*10^(-1)),line(2.61979765,0,2.61979765,0.03233290),line(2.71979765,0,2.71979765,0.24756935*10^(-1)),line(2.81979765,0,2.81979765,0.18767486*10^(-1)),line(2.91979765,0,2.91979765,0.01408550),line(3.01979765,0,3.01979765,0.10466361*10^(-1)),line(3.11979765,0,3.11979765,0.76997402*10^(-2)),line(3.21979765,0,3.21979765,0.56080711*10^(-2)),line(3.31979765,0,3.31979765,0.40439707*10^(-2)),line(3.41979765,0,3.41979765,0.28870849*10^(-2)),line(3.51979765,0,3.51979765,0.20406483*10^(-2)),line(3.61979765,0,3.61979765,0.14280184*10^(-2)),line(3.71979765,0,3.71979765,0.98936495*10^(-3)),line(3.81979765,0,3.81979765,0.67863506*10^(-3)),line(3.91979765,0,3.91979765,0.46086435*10^(-3)),line(4.01979765,0,4.01979765,0.30986105*10^(-3)),line(4.11979765,0,4.11979765,0.20626138*10^(-3)),line(4.21979765,0,4.21979765,0.13593332*10^(-3)),line(4.31979765,0,4.31979765,0.8869333*10^(-4)),line(4.41979765,0,4.41979765,0.57294516*10^(-4)),line(4.51979765,0,4.51979765,0.366431*10^(-4)),line(4.61979765,0,4.61979765,0.2320216*10^(-4)),line(4.71979765,0,4.71979765,0.14545267*10^(-4)),line(4.81979765,0,4.81979765,0.90275938*10^(-5)),line(4.91979765,0,4.91979765,0.5547271*10^(-5)),locate(20,20,1))}}}

e) The area to the left of z is 0.6700.

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graph(400,200,-5,5,-.5,1.5, exp(-x^2/2)),
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f) The area to the right of z is 0.3300. 

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Answers: 
a) z = 1.96 
b) z = 1.96 
c) z = 0.61 
d) z = 1.12 
e) z = 0.44 
f) z = 0.44

Edwin&lt;/pre&gt;</PRE>