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 less than 1425 µm? At least 900 µm? (Round your answers to four decimal places.)

(b) What is the probability that the size of a single droplet is between 900 and 1425 µm? (Round your answer to four decimal places.)


(c) How would you characterize the smallest 2% of all droplets? (Round your answer to two decimal places.)

The smallest 2% of droplets are those smaller than __ µm in size.

(d) If the sizes of five independently selected droplets are measured, what is the probability that at least one exceeds 1425 µm? (Round your answer to four decimal places.)

Explanation / Answer

SolutionA:

mean=1050

stddev=150

P(X<1425)

z=x-mean/sd

=1425-1050/150

=375/150

=2.5

P(z<2.5)

=0.9938

ANSWER:0.9938

? At least 900 µm

P(X>=900)

z=900-1050/150

=- 150/150

=-1

P(z>=1)=0.8413

answer 0.8413

Solutionb:

(b) What is the probability that the size of a single droplet is between 900 and 1425 µm? (Round your answer to four decimal places.)

P(900<X<1425)

for X=900

z=900-1050/150

=-150/150

=-1

P(X=1425)

z=1425-1050/150

z=2.5

P(-1<z<2.5)

=P(Z<2.5)-P(z<-1)

=0.9938-0.1587

=0.8351

Solutionc:

we have P(Z<-2.05)=0.02=2%

z=x-mean/sd

-2.05=x-1050/150

-2.05*150+1050=x

x=742.5

ANSWER 742.5

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