find the probabilities Use a calculator and the Ztable in yo

Use a calculator and the Z-table in your text to solve the following items. Round Z-scores to 2 decimal places. Do not round table values. A normally distributed population has a mean of 337 and a standard deviation of 83 Convert X to Z: If X = 490.55 Z = 1.85 If Z = 103.77 Z = -2.81 If X = 311.27 Z= -0.31 If X = 503 z = 7 Convert Z to X: if Z = -2.68 x = 114.560 if Z = 0 X = 337 if Z = 1.15 X = 432.45 if Z = -1.15 X = 241.55 Find the probabilities: P( x = 435.77 ) = 0.1170 P ( X

Solution

9.

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    435.77      
u = mean =    337      
          
s = standard deviation =    83      
          
Thus,          
          
z = (x - u) / s =    1.19      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   1.19   ) =    0.882976804 [ANSWER]

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10)

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    435.77      
u = mean =    337      
          
s = standard deviation =    83      
          
Thus,          
          
z = (x - u) / s =    1.19      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   1.19   ) =    0.117023196 [ANSWER]

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11)

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    238.23      
u = mean =    337      
          
s = standard deviation =    83      
          
Thus,          
          
z = (x - u) / s =    -1.19      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   -1.19   ) =    0.117023196 [ANSWER]

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12.

We first get the z score for the two values. As z = (x - u) / s, then as          
x1 = lower bound =    124.52      
x2 = upper bound =    549.48      
u = mean =    337      
          
s = standard deviation =    83      
          
Thus, the two z scores are          
          
z1 = lower z score = (x1 - u)/s =    -2.56      
z2 = upper z score = (x2 - u) / s =    2.56      
          
Using table/technology, the left tailed areas between these z scores is          
          
P(z < z1) =    0.005233608      
P(z < z2) =    0.994766392      
          
Thus, the area between them, by subtracting these areas, is          
          
P(z1 < z < z2) =    0.989532784   [ANSWER]  

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