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 pm and standard deviation 150 pm was a reasonable model for droplet size for water (the "control treatment") sprayed through a 760 ml/min nozzle. What is the probability that the size of a single droplet is less than 1500 mu m? At least 975 mu m? (Round your answers to four decimal places.) less than 1500 mu m at least 975 mu m What is the probability that the size of a single droplet is between 975 and 1500 mu m? How would you characterize the smallest 2% of all droplets? () The smallest 2% of droplets are those smaller than mu m in size. If the sizes of five independently selected droplets are measured, what is the probability that at least one exceeds 1500 mu m? (Round your answer to four decimal places.)

Explanation / Answer

Mean = 1050
Stdev = 150

a.

P(X<1500) = P(Z< 1500-1050/150) = P(Z<3) =.997
P(X>=975) = P(Z>=-(1050-975) / 150) = P(z>-.5) = .6915

b.

P(975<x<1500) = p(-.5<Z<3) = .9973-.6915 = .3058

c.

P(X=x) = .02
The Z value is -2.05
X=-2.05*150+1050=742.5

d.

P(X>=1500) = .003
P(X>=1)
=5C1(.003^1)(.997^4)+..5C5(.003^5)(.997^0)
=5C1(.003^1)(.997^4)
=0.01491

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