In the process of producing engine valves, the valves are subjected to a first grind. Valves whose thicknesses are within the specification are ready for installation. Those valves whose thicknesses are above the specification are reground, while those whose thicknesses are below the specification are scrapped. Assume that after the first grind, 74% of the valves meet the specification, 18% are reground, and 8% are scrapped. Furthermore, assume that of those valves that are reground, 88% meet the specification, and 12% are scrapped. Draw a tree diagram to represent the situationFind the probability that a valve is ground only onceGiven that a valve is not reground, what is the probability that it is scrapped?Find the probability that a valve is scrappedGiven that a valve is scrapped, what is the probability that it was ground twice?Find the probability that the valve meets the specification (after either the first or second grind).Given that a valve meets the specification (after either the first or second grind), what is the probability that it was ground twice?Given that a valve meets the specification, what is the probability that it was ground only once?

Given information:- PMeet specification=74%=74100=0.74PReground=0.18PScrap=0.08PMeet…

Answered: In the process of producing engine…

Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter12: Quadratic Functions

Section12.8: Joint And Combined Variation

Problem 3E

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In the process of producing engine valves, the valves are subjected to a first grind. Valves whose thicknesses are within the specification are ready for installation. Those valves whose thicknesses are above the specification are reground, while those whose thicknesses are below the specification are scrapped. Assume that after the first grind, 74% of the valves meet the specification, 18% are reground, and 8% are scrapped. Furthermore, assume that of those valves that are reground, 88% meet the specification, and 12% are scrapped.

Draw a tree diagram to represent the situation
Find the probability that a valve is ground only once
Given that a valve is not reground, what is the probability that it is scrapped?
Find the probability that a valve is scrapped
Given that a valve is scrapped, what is the probability that it was ground twice?
Find the probability that the valve meets the specification (after either the first or second grind).
Given that a valve meets the specification (after either the first or second grind), what is the probability that it was ground twice?
Given that a valve meets the specification, what is the probability that it was ground only once?

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