Answer: Spray drift is a constant concern for pesticide

Chapter 4, Problem 36E

(choose chapter or problem)

Get Unlimited 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?

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.

Add to cart


Study Tools You Might Need

Not The Solution You Need? Search for Your Answer Here:

×

Login

Login or Sign up for access to all of our study tools and educational content!

Forgot password?
Register Now

×

Register

Sign up for access to all content on our site!

Or login if you already have an account

×

Reset password

If you have an active account we’ll send you an e-mail for password recovery

Or login if you have your password back