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 um and standard deviation 150 um 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 1425 um? At least 950 um? (Round your answers to four decimal places.) less than 1425 um at least 950 pm 

(b) What is the probability that the size of a single droplet is between 950 and 1425 um? (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 um in size 

(d) If the sizes of five independently selected droplets are measured, what is the probability that at least one exceeds 1425 pm? (Round your answer to four decimal places.) 

Answer 1

M=1050 PIX L1425) By Normal approximation- el X ne 1425-14 Plze 1425.105 150 Plze 2L 2.5) By z table -0.9938 → Plx>,950) By Normal approximation- PM Mon 2, 950 - 950-M 950-1050 27, Pl 23 -0.67) I-Plz 2 ~0.67) By z table 0.2514 0.7486

el aro LX21425) By Part 1a) & (6) 0.9936 - 0.7466 0.2452 PIXL=0.02 OR 2% Pl Xmye stad )= 0.02 to) - Z P LC-1050 - 0.02 By 2 table Plze-2.05)= 0.02 2-1050 150 2=742.5 so below 742.5 is 2%.. pbedy x > 1425) = |- PIXL 1925) 0.9938 0.00 62 nas, p = 0.0062

By Binomial dest? PlX=K) = nx pk 11 pjh-k С Pl &>, 1) = 1r Plaku Ir PlX: 0 PlX=o) = 50 10.0062)° (0.9938) = 0.9694 Pl&>,1)= 1-0.9694 -0.0306 Please like