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In a certain type of automobile engine, the cylinder head
Chapter 2, Problem 6SE(choose chapter or problem)
In a certain type of automobile engine, the cylinder head is fastened to the block by 10 bolts, each of which should be torqued to \(60 \mathrm{~N} \cdot \mathrm{m}\). Assume that the torques of the bolts are independent.
a. If each bolt is torqued correctly with probability 0.99, what is the probability that all the bolts on a cylinder head are torqued correctly?
b. The goal is for 95% of the engines to have all their bolts torqued correctly. What must be the probability that a bolt is torqued correctly in order to reach this goal?
Equation Transcription:
Text Transcription:
60 N{cdot}m
Questions & Answers
QUESTION:
In a certain type of automobile engine, the cylinder head is fastened to the block by 10 bolts, each of which should be torqued to \(60 \mathrm{~N} \cdot \mathrm{m}\). Assume that the torques of the bolts are independent.
a. If each bolt is torqued correctly with probability 0.99, what is the probability that all the bolts on a cylinder head are torqued correctly?
b. The goal is for 95% of the engines to have all their bolts torqued correctly. What must be the probability that a bolt is torqued correctly in order to reach this goal?
Equation Transcription:
Text Transcription:
60 N{cdot}m
ANSWER:
Step 1 of 3:
It is given that 10 bolts are used to fasten a cylinder head to a block.
It is assumed that the torques of the bolt are independent.
Using these,we have to find the required probabilities.