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.

(b) What is the probability that the size of a single droplet is between 925 and 1350 µm? (Round your answer to four decimal places.)

Explanation / Answer

NORMAL DISTRIBUTION
the PDF of normal distribution is = 1/ * 2 * e ^ -(x-u)^2/ 2^2
standard normal distribution is a normal distribution with a,
mean of 0,
standard deviation of 1
equation of the normal curve is ( Z )= x - u / sd ~ N(0,1)
mean ( u ) = 1050
standard Deviation ( sd )= 150
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 925) = (925-1050)/150
= -125/150 = -0.8333
= P ( Z <-0.8333) From Standard Normal Table
= 0.2023
P(X < 1350) = (1350-1050)/150
= 300/150 = 2
= P ( Z <2) From Standard Normal Table
= 0.9772
P(925 < X < 1350) = 0.9772-0.2023 = 0.7749

the probability that the size of a single droplet is between 925 and 1350 µm is 0.7749

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