If X has a normal distribution with mean mu 90 and standard

If X has a normal distribution with mean, mu = 90 and standard deviation, T = 3 What is the probability xGE92?

Solution

A)

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    92      
u = mean =    90      
          
s = standard deviation =    3      
          
Thus,          
          
z = (x - u) / s =    0.666666667      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   0.666666667   ) =    0.252492538 [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 =    88      
x2 = upper bound =    92      
u = mean =    90      
          
s = standard deviation =    3      
          
Thus, the two z scores are          
          
z1 = lower z score = (x1 - u)/s =    -0.666666667      
z2 = upper z score = (x2 - u) / s =    0.666666667      
          
Using table/technology, the left tailed areas between these z scores is          
          
P(z < z1) =    0.252492538      
P(z < z2) =    0.747507462      
          
Thus, the area between them, by subtracting these areas, is          
          
P(z1 < z < z2) =    0.495014925   [ANSWER]