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 1485 µm? At least 1000 µm? (Round your answers to four decimal places.)

(b) What is the probability that the size of a single droplet is between 1000 and 1485 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 1485 µm? (Round your answer to four decimal places.)

less than 1485 µm      at least 1000 µm

Explanation / Answer

a)

probability that the size of a single droplet is less than 1485 µm:

At least 1000 µm:

b)

  probability that the size of a single droplet is between 1000 and 1485 µm:

c)

for smallest 2% ; critical z =-2.05

hence size =mean+z*std deviation =1050-2.05*150 =742.50

d) probability that at least one exceeds 1485 µm =1-P(none exceed 1485)=1-(0.9981)5 =0.0095

for normal distribution z score =(X-)/ here mean=       = 1050 std deviation   == 150.000

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