The Virginia cooperative extension reports that the mean weight of yearling Angu

Question

The Virginia cooperative extension reports that the mean weight of yearling Angus steers is 1152 pounds. Suppose that weights of all such animals can be described by a normal curve with a standard deviation of 84 pounds. What percentage of angus steers weigh between 1000 and 1200 pounds The Virginia cooperative extension reports that the mean weight of yearling Angus steers is 1152 pounds. Suppose that weights of all such animals can be described by a normal curve with a standard deviation of 84 pounds. What percentage of angus steers weigh between 1000 and 1200 pounds

Explanation / Answer

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    1100      
u = mean =    1152      
          
s = standard deviation =    84      
          
Thus,          
          
z = (x - u) / s =    -0.619047619      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   -0.619047619   ) =    0.267942495 or 26.79% [ANSWER]

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