Question 1. Suppose droplet size for water sprayed through a certain type of noz

Question

Question 1. Suppose droplet size for water sprayed through a certain type of nozzle is normally distributed with mean 1200 m and standard deviation 150 m. Give your answers to four decimal places. A. What is the probability that the size of a single droplet is less than 1200 m? (4pts) B. What is the probability that the size of a single droplet is more than 900 um? (3pts) C. What is the probability that the size of a single droplet is between 900 and 1200 m? (3pts) D. Find the 75th percentile of droplet size. (4pts) E. Find the droplet size such that 98% of droplets are larger than this value. (4pts)

Explanation / Answer

A) P(X < 1200)

= P(z < (1200 - 1200)/150)

= P(z < 0)

= 0.5

b) P(X > 900)

= P(z > (900 - 1200)/150)

= P(z > -2)

= 0.9772

c) P(900 < X < 1200)

= P(-2 < z < 0)

= P(z < 0) - P(z < -2)

= 0.5 - 0.0228

= 0.4772

d) For 75th percentile, z = 0.67

Hence,

X = 1200 + 0.67*150 = 1300.50

e) For 98% of the area to the right, z value = -2.05

Hence,

Droplet size = 1200 - 2.05*150 = 892.50

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