Question

pray 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 µm and standard deviation 150 µm was a reasonable model for droplet size for water (the “control treatment†) sprayed through a 760 ml/min nozzlec) what is the probability that at least one exceeds 1500 µm? (d) what is the probability that exactly two of these five selected droplets exceed 1500 µm?

Answer 1

Here we have

The z-score for X = 1500 is

The probability that a droplet exceeds 1500 µm is

(a)

Let Y is shows the number of droplets out of 5 exceeds 1500  µm. Here Y has binomial distribution with parameter n=5 and p=0.0013.

The probability that at least one exceeds 1500 µm is

(b)

The probability that exactly two of these five selected droplets exceed 1500 µm is