The mean weight of trucks traveling on a particular section

The mean weight of trucks traveling on a particular section of I-475 is not known. A state highway inspector needs an estimate of the mean. He selects a random sample of 49 trucks passing the weighing station and finds the mean is 17.3 tons, with a standard deviation of the sample of 4.6 tons. What is probability that a truck will weigh less than 15.4 tons?

Solution

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    15.4      
u = mean =    17.3      
          
s = standard deviation =    4.6      
          
Thus,          
          
z = (x - u) / s =    -0.413043478      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   -0.413043478   ) =    0.33978738 [ANSWER]