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 Depositions 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 1485 pm? At least 975 pm? (Round your answers to four decimal places.) less than 1485 mu m at least 975 mu m (b) What is the probability that the size of a single droplet is between 975 and 1485 pm? (Round your answer to four decimal places.) (c) How would you characterize the smallest 2% of all droplets? The smallest 2% of droplets are those smaller than mu m in size. (d) If the sizes of five independently selected droplets arc measured, what is the probability that at least one exceeds 1485 mu m? (Round your answer to four decimal places.)

Explanation / Answer

a)less then 1485 micrometer =P(X<1485)=P(Z<(1485-1050)/150)=P(Z<2.9)=0.9981

at least 975 micrometer =P(X>975)=1-P(Z<(975-1050)/150)=1-P(Z<-0.5)=1-0.3085=0.6915

b)P(975<X<1485)=P(-0.5<Z<2.9)=0.9981-0.3085=0.6896

c)for smallest 2%; z=-2.0537

hence corresponding size =1050-2.0537*150=741.95

d)for n=5; std error =std deviation/(n)1/2 =67.082

henc eP(X>1485)=1-P(X<1485)=1-P(Z<(1485-1050)/67.082)=1-P(Z<6.4846)=1-1=0.0000

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