The following is the distribution of the daily number of power failures reported in an urbanized city in the Visayas: Number of power failures O Number of days 17 1 78 2 54 3 4 22 8 5 6 7 S 3 2 8 9 1 O The electrical engineer employed by the Dept of Energy in the city made the claim that the daily occurrences of power failures follows a Poisson distribution. a) Determine the parameter λ and state the appropriate Poisson distribution function. b) Determine the empirical (i.e. observed) probability of getting at most 2 power failures in a day, and compare this probability with the Poisson distributed probability by showing the percentage difference of the empirical probability from the theoretical Poisson probability. c) Determine the empirical probability of having 3 to 5 power failures in a day and compare this probability with the Poisson distribution function probability. Again, showing the percentage difference between the empirical and Poisson.

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