3. In 1984, the ISO (International Organization for Standardization) suggested a serviceabil- ity standard for a...
3. In 1984, the ISO (International Organization for Standardization) suggested a serviceabil- ity standard for a general-purpose building against wind-induced vibrations such that the root-mean-square (RMS) of the building's acceleration time history should be less than 2.89 cm/sec2 for comfortable environment. Consider a high-rise building in Chicago which is subjected to strong winds all year long. Suppose the RMS of the building's acceleration exceeds 2.89 cm/sec2 for average 25 days per year and hence people would found it uncomfortable working in the building for those days. Let us assume the arrivals of uncomfortable days can be modeled as a Poisson process. (a) What is the mean occurrence rate (in /day) of uncomfortable days? For convenience of the analysis, let us disregard years with 366 days. (b) Average inter-arrival time between uncomfortable days? (c) Compute the probability that there will be more than three uncomfortable days during a month with 31 days.