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"t investigated the effects of herbicide formulation on spray atomization. A figure in a paper suggested the normal distribution with mean 1050 pm and standard deviation 150 |jm was a reasonable model for droplet size for water (the "control treatment") sprayed through a 760 ml/min nozzle. What is the probability that the size of a single droplet is less than 1425 pm? At least 950 pm? (Roand your answers to four decimal places.) What is the probability that the size of a single droplet is between 950 and 1425 pm? (Roand your answer to four decimal places.) How would you characterize the smallest 2% of all droplets? (Roand your answer to two decimal places.) If the sizes of five independently selected droplets are measured, what is the probability that at least one exceeds 1425 pm? (Roand your answer to four decimal places.)

Explanation / Answer

mean = 1050

standard dev = 150

a) 1)

For x = 1425, the z-value z = (1425 - 1050) /150 = 2.5

Hence P(x < 1425) = P(z < 2.5) = [area to the left of 2.5] = 0.9938

2)

For x = 950, z = (950 - 1050) /150 = 0.66

Hence P(x > 950) = P(z > 0.66) = [total area] - [area to the left of 0.66]

= 1 - 0.7454 = 0.2546

b)

For x = 950 , z = (950 - 1050) / 150 = -0.66 and for x = 1425, z = (1425 - 1050) / 150 = 2.5

Hence P(950 < x < 1425) = P(0.66 < z < 2.5) = [area to the left of z = 2.5] - [area to the left of -0.66]

= 0.9938 - 0.2546 = 0.7392

c) for z 0.02

score = -2.5

x = mean +z*standard dev

= 1050 + (-2.5)*150 = 675

d)

For x = 1425, z = (1425 - 1425) / 150 = 0

Hence P(x > 1425) = P(z > 0) = [total area] - [area to the left of 0]

= 1 - 0.5 = 0.5

so atleast one exceed among 5 =1 - NO ONE EXCEED

5C0*(0.5)^5 = 0.031

1-0.031 = 0.969

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