Birth hospital are normally distributed with a mean of 3421

Birth hospital are normally distributed with a mean of 3421 g and a standard deviation of 495 g. If a hospital plans to set up observation conditions for the lightest 4% of babies, what weight is used for the cut-off separating the lightest 4% from the others?

Solution

First, we get the z score from the given left tailed area. As          
          
Left tailed area =    0.04      
          
Then, using table or technology,          
          
z =    -1.750686071      
          
As x = u + z * s,          
          
where          
          
u = mean =    3421      
z = the critical z score =    -1.750686071      
s = standard deviation =    495      
          
Then          
          
x = critical value =    2554.410395 = 2554 GRAMS [ANSWER]