Question 1179110
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Hi
distribution approximately normal with µ = 525 and σ = 30
The area in Red P(510 < x < 540) can be found by calculating P(x ≤ 540) - P(x ≤ 510)
*[illustration graph_4_23.jpg].
Using z -values, |{{{z =blue (x - mu)/blue(sigma)}}}
knowing P is always the area to the left of the z-value: 
 P(z ≤ (15)/30) - P( z ≤ (-15)/30)  Use tables to determine P(Z-values) for subtraction:
0r
 Using a TI calculator 0r similarly a Casio fx-115 ES plus
Takes seconds:
P(510 < x < 540) = normalcdf(510,540,525,30) = .3829

Important You are comfortable using Your calculator.  
Wish You the Best in your Studies.
Standard Normal Curve with various z-values
{{{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))}}}
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