To help students improve their reading a school district de

. To help students improve their reading, a school district decides to implement a reading program. It is to be administered to the bottom 15% of the students in the district, based on the scores on a reading achievement exam given in the child’s dominant language. The readingscore for the pooled students in the district is approximately normally distributed with a mean of 122 points, and standard deviation of 18 points.

a. What fraction of students score above 140 points?

b. Find the cutoff score that will make a student eligible for the program

Solution

a)

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    140      
u = mean =    122      
          
s = standard deviation =    18      
          
Thus,          
          
z = (x - u) / s =    1      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   1   ) =    0.158655254 [ANSWER]
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B)

First, we get the z score from the given left tailed area. As          
          
Left tailed area =    0.15      
          
Then, using table or technology,          
          
z =    -1.036433389      
          
As x = u + z * s,          
          
where          
          
u = mean =    122      
z = the critical z score =    -1.036433389      
s = standard deviation =    18      
          
Then          
          
x = critical value =    103.344199   [ANSWER]