A what proportion of babies born full term are low birth wei

A) what proportion of babies born full term are low birth weight babies?

B) What proportion of babies born full term are very low birth weight babies?

Solution

a)

We first get the z score for the two values. As z = (x - u) / s, then as          
x1 = lower bound =    1500      
x2 = upper bound =    2500      
u = mean =    3350      
          
s = standard deviation =    440      
          
Thus, the two z scores are          
          
z1 = lower z score = (x1 - u)/s =    -4.204545455      
z2 = upper z score = (x2 - u) / s =    -1.931818182      
          
Using table/technology, the left tailed areas between these z scores is          
          
P(z < z1) =    1.30804E-05      
P(z < z2) =    0.026690976      
          
Thus, the area between them, by subtracting these areas, is          
          
P(z1 < z < z2) =    0.026677895   [ANSWER]

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B)

  
We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    1500      
u = mean =    3350      
          
s = standard deviation =    440      
          
Thus,          
          
z = (x - u) / s =    -4.204545455      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   -4.204545455   ) =    0.0000130804 [ANSWER]