The mean weight of loads of rock is 470 tons with a standard

The mean weight of loads of rock is 47.0 tons with a standard deviation of 6.0 tons. If 16 loads are chosen at random for a weight check, find the probability that the mean weight of those loads is less than 46.2 tons.

Select one:

a. 44.04%

b. 29.69%

c. 71.31%

d. 55.96%

e. Cannot be determined

Solution

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    46.2      
u = mean =    47      
n = sample size =    16      
s = standard deviation =    6      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    -0.533333333      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   -0.533333333   ) =    0.296901429 = 29.69% [ANSWER, OPTION B]