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 ?m and standard deviation 150 ?m 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 ?m ? At least 1000?m ? b.? ?What is the probability that the size of a single droplet is between 1000 ?m and ? c.? ow 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 1500?m?

Answer: Step1 of 5: Given the normal distribution with mean = 1050m and standard deviation = 150 m. A continuous random variable ‘x’ is said to have a normal distribution with parameter and .The pdf of x is The notation is X ~ N(,) Step2 of 5: a). To find the probability that the size of a single droplet is i).less than 1500m and ii). At least 1000 m. x 15001050 i). P(x < 1500) = P( < 150 ) = 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 m is 0.9987. x 10001050 ii). P(x > 1000) ( > 150 ) = 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 m is 0.6293. Step3 of 5: b). To determine the probability that the size of a single droplet is between 1000 and 1500. P(1000 X 1500) = (1500) - (1000) = ( 15001050 x 10001050) 150 150 = (3Z -0.33) = 0.9987 - 0.3707 ( this value from standard normal table) = 0.628. Thus,the probability that the size of a single droplet is between 1000 and 1500 is 0.628....