Problem 4. [5+4+8+8+5 = 30 points] Spray drift is a constant concern for pesticide applicators and agricultural procedures. 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 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 1500 um? At least 1000 um? (b) what is the probability that the size of a single droplet is between 1000 and 1500 um? If the sizes of five independently selected droplets are measured, find the probability that (c) at least one of these five selected droplets has a size between 1000 and 1500 um? (d) exactly two of these five selected droplets have size between 1000 and 1500 um? (e) each of these five selected droplets has a size between 1000 and 1500 um