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 mu m and standard deviation 150 mu m 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 less than 1440 mu m? At least 1000 mu m? less than 1440 mu m .9953 at least 1000 mu m .6179 (b) What is the probability that the sue of a single droplet is between 1000 and 1440 mu m? 0.3774 (c) How would you characterize the smallest 2% of all droplets? The smallest 2% of droplets are those smaller than 618 mu m in size. (d) If the sizes of five independently selected droplets are measured, what is the probability that at least one exceeds 1440 mu m? You may need to use the appropriate table in the Appendix of Tables to answer this question.

Explanation / Answer

a)P(X<1440)=P(Z<(1440-1050)/150)=P(Z<2.6)=0.9953

b)P(X>1000)=1-P(X<1000)=1-P(Z<-0.3333)=1-0.3694=0.6306

b)P(1000<X<1440)=0.9953-0.3694=0.6259

c) for lowest 2% ; z=-2.0537

hence corresponding value =mean +z*std deviation =741.94

d)probabilty that at least one exceed =1-P(none exceed)=1-(0.9953)5 =1-0.9769=0.0231

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