Question

A farmer believes that the yields of his tomato plants have a normal distribution with an average yield of 11 lbs and a standard deviation of 2.1 lbs. The farmer would like to identify the plants which yield the highest 5% in weight and save them for breeding purposes. What yielded weight separates the top 5% of the crop from the rest? Use the information above and the Z table to find the Z SCORE that you will use in this problem.

Answer 1

Given:
mean, μ = 11 lb
Std. deviation, σ = 2.1

Let x =  the weight that separates the top 5% of the crop.
The z-score is
z = (x - μ)/σ 
   = (x - 11)/2.1

From standard z-table for normal distribution,
P(z=1.645) = 0.95
 
Therefore
(x - 11)/2.1 = 1.645
x - 11 = 1.645/2.1 = 0.7833
x = 11.783

Answer:  11.8 lb (nearest tenth)