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Answer: Spray drift is a constant concern for pesticide
Chapter 4, Problem 36E(choose chapter or problem)
Problem 36E
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” (Weed Technology, 2005: 1030–1036) investigated the effects of herbicide formulation on spray atomization. A figure in the 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 1000μm ?
b. What is the probability that the size of a single droplet is between 1000 μm and ?
c. How would you characterize the smallest 2% of all droplets?
d. If the sizes of five independently selected droplets are measured, what is the probability that at least one exceeds 1500μm?
Questions & Answers
QUESTION:
Problem 36E
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” (Weed Technology, 2005: 1030–1036) investigated the effects of herbicide formulation on spray atomization. A figure in the 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 1000μm ?
b. What is the probability that the size of a single droplet is between 1000 μm and ?
c. How would you characterize the smallest 2% of all droplets?
d. If the sizes of five independently selected droplets are measured, what is the probability that at least one exceeds 1500μm?
ANSWER:
Answer:
Step1 of 5:
Given the normal distribution with mean = 1050 and standard deviation .
A continuous random variable ‘x’ is said to have a normal distribution with parameter and The pdf of x is
The notation is
Step2 of 5:
a). To find the probability that the size of a single droplet is i).less than 1500 and ii). At least 1000 .
i). P(x < 1500) = P(
= P(z < 3)
= 0.9987 ( this value from standard normal table)
Thus, the probability that the size of a single droplet is less than 1500 is 0.9987.
ii). P(x > 1000) = P(
= P(z > -0.33)
= 1- P(z < -0.33)
= 1- 0.3707 ( this value from standard normal table)
= 0.6293.
Thus,the probability that the size of a single droplet is At least 1000 is 0.6293.
Step3 of 5:
b). To determine the probability that the size of a single droplet is between 1000 and 1500.