Question 870607
Convert the raw score of x = 1140 to a standard z-score


z = (x-mu)/sigma
z = (1140-1200)/75
z = -0.80



Now use <a href="http://www.math.upenn.edu/~chhays/zscoretable.pdf">this table</a> to find the area to the left of z = -0.80


That area is 0.2119. Let's call this area1


------------------------------------------------------------------------------------------


Convert the raw score of x = 1260 to a standard z-score


z = (x-mu)/sigma
z = (1260-1200)/75
z = 0.80




Now use <a href="http://www.math.upenn.edu/~chhays/zscoretable.pdf">this table</a> to find the area to the left of z = 0.80


That area is 0.7881. Let's call this area2


------------------------------------------------------------------------------------------


Now subtract the two areas: 


Area2 - Area1 = 0.7881 - 0.2119 = 0.5762


The area between z = -0.80 and z = 0.80 is approximately 0.5762


So the area between x = 1140 and x = 1260 is also approximately 0.5762


That means the probability is about <font color="red">0.5762</font> (roughly 57.62%)