will rate thank you The weight of a 5th grader is normally d

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The weight of a 5th grader is normally distributed with a mean of 82 pounds and a variance of 94 pounds^2. Let weight, in pounds, be represented by random variable X.

P(77 < X < x2) = 0.128. Find x2

Solution

We first get the left tailed area of 77 lbs:

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    77      
u = mean =    82      
          
s = standard deviation =    9.695359715      
          
Thus,          
          
z = (x - u) / s =    -0.515710623      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   -0.515710623   ) =    0.303028267
          
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Thus, the left tailed area of x2 is 0.128 + 0.303028267 = 0.431028267.

To get x2, first, we get the z score from the given left tailed area. As          
          
Left tailed area =    0.431028267      
          
Then, using table or technology,          
          
z =    -0.173756879      
          
As x2 = u + z * s,          
          
where          
          
u = mean =    82      
z = the critical z score =    -0.173756879      
s = standard deviation =    9.695359715      
          
Then          
          
x2 = critical value =    80.31536455   [ANSWER]