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

Question

Quizplus · Accepted Answer

To find the number of plants that produced peppers weighing between 13 and 16 pounds, we need to find the area under the normal curve between those two weights. We can standardize those weights by subtracting the mean and dividing by the standard deviation:

For 13 pounds: (13 - 15) / 1.75 = -1.14
For 16 pounds: (16 - 15) / 1.75 = 0.57

We can then use a standard normal distribution table (or a calculator or software) to find the proportion of the area under the curve between -1.14 and 0.57:

P(-1.14 < Z < 0.57) = 0.4938

This means that about 49.38% of the plants produced peppers in this weight range. To find the number of plants, we can multiply this proportion by the total number of plants in the experiment:

0.4938 * 200 = 98.76

Rounding to the nearest whole number, we get:

Answer: B (118)

The Seasonal Output of a New Experimental Strain of Pepper