5. For a construction project, a large mumber of bolts in one batch is purchased. It is known from the past experience that the tensile strength of each bolt can be modeled by a lognormal distribution with a mean value of µx = 350 kN and a coefficient of variation of 8g = 0.15. In a load test, a bolt is considered to be acceptable if it carries at least 270 KN. a) What is the probability that a bolt picked randomly will pass the test? b) It is impractical to test all the bolts for their strengths. Therefore, for quality control purposes, it is required that all of the 5 bolts selected at random from the batch must pass the test for the whole batch to be acceptable. In this case, what is the probability that the purchased batch is rejected (not suitable)? c) Apart from the inspection scheme applied in Part b, another inspection scheme is proposed in order to accept the purchased batch. In this new inspection scheme, at least 9 of the 10 bolts tested must pass the test for the whole batch to be acceptable. Is this new inspection scheme stricter than the one used in Part b?

5. For a construction project, a large mumber of bolts in one batch is purchased. It is known from the past experience that the tensile strength of each bolt can be modeled by a lognormal distribution with a mean value of µx = 350 kN and a coefficient of variation of 8g = 0.15. In a load test, a bolt is considered to be acceptable if it carries at least 270 KN. a) What is the probability that a bolt picked randomly will pass the test? b) It is impractical to test all the bolts for their strengths. Therefore, for quality control purposes, it is required that all of the 5 bolts selected at random from the batch must pass the test for the whole batch to be acceptable. In this case, what is the probability that the purchased batch is rejected (not suitable)? c) Apart from the inspection scheme applied in Part b, another inspection scheme is proposed in order to accept the purchased batch. In this new inspection scheme, at least 9 of the 10 bolts tested must pass the test for the whole batch to be acceptable. Is this new inspection scheme stricter than the one used in Part b?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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