4 Suppose the grades of particular exam is rormally distrib

4. Suppose the grades of . particular exam is rormally distributed with mean -5 deviation 10. Using the above information, answer the following questions. 0 and standard the follkowing qpuestions 125 points a) What is the prohihility that a student\'s grade is more than 5cr, ismore than SC? ,U-50 -50 b) What is the probability that a student\'s grade is between 40 and 50? b) What is the probabälity thas a student\'s grade is between 40 what is the probability thata student\'s grade is less than 70?

Solution

a)

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    50      
u = mean =    50      
          
s = standard deviation =    10      
          
Thus,          
          
z = (x - u) / s =    0      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   0   ) =    0.5 [ANSWER]

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b)

We first get the z score for the two values. As z = (x - u) / s, then as          
x1 = lower bound =    40      
x2 = upper bound =    50      
u = mean =    50      
          
s = standard deviation =    10      
          
Thus, the two z scores are          
          
z1 = lower z score = (x1 - u)/s =    -1      
z2 = upper z score = (x2 - u) / s =    0      
          
Using table/technology, the left tailed areas between these z scores is          
          
P(z < z1) =    0.158655254      
P(z < z2) =    0.5      
          
Thus, the area between them, by subtracting these areas, is          
          
P(z1 < z < z2) =    0.341344746   [ANSWER]

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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]