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The factor of safety, F,, of a rock slope is commonly thought of as the ratio of the maximum load or stress that a slope can sustain to the actual maximum load or stress that is applied during a design lifetime. Suppose that an extensive statistical study has determined that the actual F, for rock slopes in the Cape Breton Highlands against sliding has a Weibull distribution with median 2.947 and 3 = 0.3. a) What is A for this distribution? b) What is the probability that the F, is less than 1 for a randomly selected rock slope? c) Suppose that design standards are such that slopes having factors of safety in excess of 2.0 are considered to be "safe". What fraction of rock slopes in the Cape Breton Highlands would then be considered "unsafe" and so thus in need of remediation?

The factor of safety, F,, of a rock slope is commonly thought of as the ratio of the maximum load or stress that a slope can sustain to the actual maximum load or stress that is applied during a design lifetime. Suppose that an extensive statistical study has determined that the actual F, for rock slopes in the Cape Breton Highlands against sliding has a Weibull distribution with median 2.947 and 3 = 0.3. a) What is A for this distribution? b) What is the probability that the F, is less than 1 for a randomly selected rock slope? c) Suppose that design standards are such that slopes having factors of safety in excess of 2.0 are considered to be "safe". What fraction of rock slopes in the Cape Breton Highlands would then be considered "unsafe" and so thus in need of remediation?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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4) The factor of safety, F, of a rock slope is commonly thought of as the ratio of the maximum load or stress that a slope can sustain to the actual maximum load or stress that is applied during a design lifetime. Suppose that an extensive statistical study has determined that the actual F for rock slopes in the Cape Breton Highlands against sliding has a Weibull distribution with median 2.947 and 3 = 0.3. a) What is A for this distribution? b) What is the probability that the F, is less than 1 for a randomly selected rock slope? c) Suppose that design standards are such that slopes having factors of safety in excess of 2.0 are considered to be "safe". What fraction of rock slopes in the Cape Breton Highlands would then be considered "unsafe" and so thus in need of remediation?
Transcribed Image Text:4) The factor of safety, F, of a rock slope is commonly thought of as the ratio of the maximum load or stress that a slope can sustain to the actual maximum load or stress that is applied during a design lifetime. Suppose that an extensive statistical study has determined that the actual F for rock slopes in the Cape Breton Highlands against sliding has a Weibull distribution with median 2.947 and 3 = 0.3. a) What is A for this distribution? b) What is the probability that the F, is less than 1 for a randomly selected rock slope? c) Suppose that design standards are such that slopes having factors of safety in excess of 2.0 are considered to be "safe". What fraction of rock slopes in the Cape Breton Highlands would then be considered "unsafe" and so thus in need of remediation?
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