c What is the probability that a students grade is less than

c) What is the probability that a student\'s grade is less than 70? 8) What is the probability that a student\'s grade is between 70 and 8o? e) Calculate the 90h percentile of grades

Solution

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c)

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    70      
u = mean =    50      
          
s = standard deviation =    10      
          
Thus,          
          
z = (x - u) / s =    2      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   2   ) =    0.977249868 [ANSWER]
  
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d)

We first get the z score for the two values. As z = (x - u) / s, then as          
x1 = lower bound =    70      
x2 = upper bound =    80      
u = mean =    50      
          
s = standard deviation =    10      
          
Thus, the two z scores are          
          
z1 = lower z score = (x1 - u)/s =    2      
z2 = upper z score = (x2 - u) / s =    3      
          
Using table/technology, the left tailed areas between these z scores is          
          
P(z < z1) =    0.977249868      
P(z < z2) =    0.998650102      
          
Thus, the area between them, by subtracting these areas, is          
          
P(z1 < z < z2) =    0.021400234   [ANSWER]

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e)

First, we get the z score from the given left tailed area. As          
          
Left tailed area =    0.90
          
Then, using table or technology,          
          
z =    1.281551566      
          
As x = u + z * s,          
          
where          
          
u = mean =    50      
z = the critical z score =    1.281551566      
s = standard deviation =    10      
          
Then          
          
x = critical value =    62.81551566   [ANSWER]