Question

Find the area of the shaded region. The graph to the right depicts IQ scores of? adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15. 108132 A symmetric bell-shaped curve is plotted over a horizontal scale. Two vertical lines run from the scale to the curve at labeled coordinates 108 and 132, which are both to the right of the curve’s center and peak. The area under the curve between the vertical lines is shaded. The area of the shaded region is nothing. ?(Round to four decimal places as? needed.)

Answer 1

Solution:

We first get the z score for the two values. As z = (x - u) / s, then as   
x1 = lower bound = 108   
x2 = upper bound = 132   
u = mean = 100   
  
s = standard deviation = 15   
  
Thus, the two z scores are   
  
z1 = lower z score = (x1 - u)/s = 108-100/15 = 0.53   
z2 = upper z score = (x2 - u) / s = 132-100/15 = 2.13   
  
Using table/technology, the left tailed areas between these z scores is   
  
P(z < z1) = 0.7019   
P(z < z2) = 0.9834   
  
Thus, the area between them, by subtracting these areas, is   
  
P(z1 < z < z2) = 0.2815