The weights of 6 month old Labrador retriever puppies are no

The weights of 6 month old Labrador retriever puppies are normally distributed with mean 45 lb. and standard deviation 6 lb. A sample of 16 puppies will be taken. What is the probability that the weight of the first puppy will be less than 44 lbs?

Solution

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    44      
u = mean =    45      
          
s = standard deviation =    6      
          
Thus,          
          
z = (x - u) / s =    -0.166666667      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   -0.166666667   ) =    0.433816167 [ANSWER]