Spray drift is a constant concern for pesticide applicators and agricultural pro

Question

Spray drift is a constant concern for pesticide applicators and agricultural producers. The inverse relationship between droplet size and drift potential is well known. The paper "Effects of 2,4-D Formulation and Quinclorac on Spray Droplet Size and Deposition"† investigated the effects of herbicide formulation on spray atomization. A figure in a paper suggested the normal distribution with mean 1050 µm and standard deviation 150 µm was a reasonable model for droplet size for water (the "control treatment") sprayed through a 760 ml/min nozzle.

(a) What is the probability that the size of a single droplet is between 950 and 1380 µm? (Round your answer to four decimal places.)

(b) If the sizes of five independently selected droplets are measured, what is the probability that at least one exceeds 1380 µm? (Round your answer to four decimal places.)

Explanation / Answer

(a)For x1=950

Z1=(x-)/=(950-1050)/150

=-0.67

X2=1380,

Z2=(x-)/=(1380-1050)/150=2.2

P(950<x<1380)=P(x1<1380)-P(x2<1050)

=P(z1<2.2)-P(z2<-0.67)

=0.9783-0.2514

=0.7269

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