The seasonal output of a new experimental strain of pepper plants was carefully weighed. The mean weight per plant is 15.0 pounds, and the standard deviation of the normally 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 choices are correct

Question

Quizplus · Accepted Answer

To find the number of plants producing between 13 and 16 pounds, calculate the z-scores for 13 and 16 pounds, then find the proportion of the normal distribution between these z-scores. The z-score for 13 is (13-15)/1.75 = -1.14, and for 16 is (16-15)/1.75 = 0.57. Using the standard normal distribution table, the proportion between these z-scores is approximately 0.591. Therefore, 0.591 * 200 = 118.2, which rounds to 118 plants.

The Seasonal Output of a New Experimental Strain of Pepper