Spray drift is a constant concern for pesticide on Spray Droplet Size and Deposi

Question

Spray drift is a constant concern for pesticide on Spray Droplet Size and Deposition t investigated the effects of herbicide formulation on spray atomization. Afigure in a paper suggested the nom al distribution with mean 1050 m and standard deviation 150 a reasonable model for droplet size for water (the "control and agricultural producers. The The paper "Effects of 2,4-D and was ) sprayed through a 760 ml/min nozzle. (a) What is the probability that the size of a single droplet is less than 1470 um? At least 950 um? (Round your answers to four decimal places.) less than 1470 um at least 950 m (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 probabity that at least one exceeds 1470 um? (Round your answer to four decimal places,) You may need to use the appropriate table in the Appendix of Tables to answer this question Need Help?

Explanation / Answer

Solution:- Given data mean = 1050m , sd = 150m,

a) => P(x < 1470) = P(Z < (x - )/)
= P(Z < (1470 - 1050)/150)
= P(Z < 2.8)
= 0.9974

=> P(x >= 950) = P(Z >= (950 - 1050)/150)
= P(Z >= -0.6667)
= 0.7486

b) P(950 < X < 1470) = P((950 - 1050)/150 < Z < (1470 - 1050)/150)
= P(-0.6667 < Z < 2.8)
= 0.746

c) P(X < x) = 0.02
x - 1050/150 = -2.054
x = 1050 - (2.0548150)
x = 741.9

d) P(x > 1470) = P(Z > 2.8)
= 0.0026

The size five independendently selected dropplets,the probability that at lest one exceeds 1470m is

P(Y >= 1) = 1 - P(Y<0)
= 0.0129

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