Final answer:
The question regarding the percentage of design faults cannot be answered without additional data. However, the referenced probability questions can be approached using the Poisson distribution if the average earthquake rate is given.
Step-by-step explanation:
The question at hand involves calculating the probabilities related to the occurrence of earthquakes in a particular year, which falls under the branch of mathematics dealing with probability and statistics.
To answer the original question about the approximate percentage of observed faults during all four phases that were design faults, there isn't enough information provided to give a precise answer. However, I can guide you on how to approach such a problem:
- First, you would need to add up all the observed faults during the four phases.
- Then, count the number of faults that have been identified as design faults.
- Divide the number of design faults by the total number of observed faults and multiply by 100 to get the percentage.
To answer the reference questions:
- c. What is the probability of zero earthquakes occurring in 2014? - To calculate this, one would typically use the Poisson distribution if the average rate of earthquakes per year is known. The Poisson probability mass function gives the probability that a given number of events occur in a fixed interval of time.
- d. What is the probability that at least two earthquakes will occur in 2014? - This can also be calculated using the Poisson distribution. The probability of at least two earthquakes is equal to 1 minus the sum of the probabilities of exactly zero and exactly one earthquake, assuming you know the average rate of earthquakes per year.