The seasonal output of a new experimental strain of pepper p

The seasonal output of a new experimental strain of pepper plants was carefully weighted. The mean weight per plant is 15.0 pounds, and the standard deviation of the nomlly distributed weights is 1.75 pounds. Of the 200 plants in the experiment, how many produced peppers weighing between 13 and 16 pounds?

A. 100

B. 118

C. 197

D. 53

E. None of the above

Solution

We first get the z score for the two values. As z = (x - u) / s, then as          
x1 = lower bound =    13      
x2 = upper bound =    16      
u = mean =    15      
          
s = standard deviation =    1.75      
          
Thus, the two z scores are          
          
z1 = lower z score = (x1 - u)/s =    -1.142857143      
z2 = upper z score = (x2 - u) / s =    0.571428571      
          
Using table/technology, the left tailed areas between these z scores is          
          
P(z < z1) =    0.126548954      
P(z < z2) =    0.716145417      
          
Thus, the area between them, by subtracting these areas, is          
          
P(z1 < z < z2) =    0.589596462      

Thus, there are 0.589596462*200 = 117.9192924 = 118 between 13 and 16 lbs.

[ANSWER: 118, OPTION B]