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A process that polishes a mirrored surface leaves an
Chapter 4, Problem 12SE(choose chapter or problem)
A process that polishes a mirrored surface leaves an average of 2 small flaws per 5 \(m^{2}\) of surface. The number of flaws on an area of surface follows a Poisson distribution.
a. What is the probability that a surface with area 3m ✕ 5m will contain more than 5 flaws?
b. What is the probability that a surface with area 2m ✕ 3m will contain no flaws?
c. What is the probability that 50 surfaces, each with dimensions 3m ✕ 6 m, will contain more than 350 flaws in total?
Equation transcription:
Text transcription:
m^{2}
Questions & Answers
QUESTION:
A process that polishes a mirrored surface leaves an average of 2 small flaws per 5 \(m^{2}\) of surface. The number of flaws on an area of surface follows a Poisson distribution.
a. What is the probability that a surface with area 3m ✕ 5m will contain more than 5 flaws?
b. What is the probability that a surface with area 2m ✕ 3m will contain no flaws?
c. What is the probability that 50 surfaces, each with dimensions 3m ✕ 6 m, will contain more than 350 flaws in total?
Equation transcription:
Text transcription:
m^{2}
ANSWER:
Answer:
Step1 of 4:
Given, a process that polishes a mirrored surface leaves an average of 2 small flaws per of surface. The number of flaws on an area of surface follows a poisson distribution.
Step2 of 4:
a). We need to find the probability that a surface with area will contain more than 5 flaws.
Let denote the number of flaws on the surface with the area
The mean concentration of flaws = so
Then the mean number of flaws in a area is 15(0.4) = 6
Therefore, the mean number of flaws for this surface is 6.
Now, find
That is,
= 1- [ P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)]