Question 879541
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Hi
Population: &#956;=100 and standard deviation &#963;=20.
 P (A < x < B) = P (z1 < z < z2) = P (z < z2) - P (z < z1)
 P (95 < x < 110) = 
P (-5/20 < z < 10/20) = P (x < .5) - P (z < .25) = .6815-.5987 = .0828
Below: find z-scores:  P (95 < x < 110) is the area under normal curve between z-values
For the normal distribution: Below:  z = 0, z = ± 1, z= ±2 , z= ±3 are plotted.  
Area under the standard normal curve to the left of the particular z is P(z)
Note: z = 0 (x value: the mean) 50% of the area under the curve is to the left and 50%  to the right
{{{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))}}}