There are seven geologic faults (and possiblymore) capable of generating a magnitude 6.7 earthquake in theregion around San Francisco. Their probabilities of rupturingby the year 2032 are 27%, 21%, 11%, 10%, 4%, 3%, and 3%.Source: Science News.a. Calculate the probability that at least one of these faults erupts by the year 2032, assuming that these are indepen-dent events. b. Scientists forecast a 62% chance of an earthquake withmagnitude at least 6.7 in the region around San Franciscoby the year 2032. Compare this with your answer from parta. Consider the realism of the assumption of independence. Also consider the role of roundoff. For example, the prob-ability of 10% for one of the faults is presumably rounded to the nearest percent, with the actual probability between9.5% and 10.5%.
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
There are seven geologic faults (and possibly
more) capable of generating a magnitude 6.7 earthquake in the
region around San Francisco. Their probabilities of rupturing
by the year 2032 are 27%, 21%, 11%, 10%, 4%, 3%, and 3%.
Source: Science News.
a. Calculate the
erupts by the year 2032, assuming that these are indepen-
dent
b. Scientists forecast a 62% chance of an earthquake with
magnitude at least 6.7 in the region around San Francisco
by the year 2032. Compare this with your answer from part
a. Consider the realism of the assumption of independence.
Also consider the role of roundoff. For example, the prob-
ability of 10% for one of the faults is presumably rounded
to the nearest percent, with the actual probability between
9.5% and 10.5%.
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