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 1500 µm? At least 925 µm? (Round your answers to four decimal places.)

(b) What is the probability that the size of a single droplet is between 925 and 1500 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 1500 µm? (Round your answer to four decimal places.)

less than 1500 µm      at least 925 µm Spray drift is a constant concern for pesticide applicators and agricultural producers. The inverse relationship betvreen 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 ?m and standard deviation 150 ?m was a reasonable model for droplet sze 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 1500 ? ? At least 925 ? m? Round your answers to four decimal places less than 1500 ?m at least 925 ?m (b) What is the probability that the size of a single droplet is between 925 and 1500 ?m? (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 1 ?m in size (d) If the sizes of five independently selected droplets are measured, what is the probability that at least one exceeds 1500 Hm? (Round your answer to four decimal places.)

Explanation / Answer

a)
mean = 1050
std.dev. = 150

z = (x - mean) / Std.deviation
P(x < 1500) = P( z < (1500-1050) / 150)
= P(z < 3) =0.9987
(From Normal probability table)

mean = 1050
std.dev. = 150

z = (x - mean) / Std.deviation
P(x > 925) = P( z > (925-1050) / 150)
= P(z > -0.8333) = 0.7977
(From Normal probability table)

b)
mean = 1050
std.dev. = 150

z = (x - mean) / Std.deviation

P( 925 < x < 1500) = P[( 925 - 1050) / 150 < Z < ( 1500 - 1050) / 150]
P( -0.8333 < Z < 3) = 0.7963

c)
From the normal distribution table, P( z < -2.05) =0.02
z = (x - mean) / std.dev
-2.05 = (x-1050)/150
solve for x
x = 1050 + (150)(-2.05) = 742.5 µm in size

d)
The probability of one droplet exceeding 1440 µm is :
mean = 1050
std.dev = 150

z = (x - mean) / std.dev
P(x > 1500) = P( z > (1500-1050) / 150)
= P(z > 3) = 1
(From Normal probability table)

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