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The downtime per day for a computing facility has mean 4 hours and standard deviation 0.9...

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Advance Math

The downtime per day for a computing facility has mean 4 hoursand standard deviation 0.9 hour. (a) Suppose that we want tocompute probabilities about the average daily downtime for a periodof 30 days. (i) What assumptions must be true to use the result ofthe central limit theorem to obtain a valid approximation forprobabilities about the average daily downtime? (Select all thatapply.) The daily downtimes must have an approximately normaldistribution. The number of daily downtimes must be greater than30. The daily downtimes must have an expected value greater thantheir variance. The daily downtimes must have the same expectedvalue and variance. The daily downtimes must be independent andidentically distributed random variables. (ii) Under theassumptions described in part (i), what is the approximateprobability that the average daily downtime for a period of 30 daysis between 1 and 5 hours? (Round your answer to four decimalplaces.) (b) Under the assumptions described in part (a), what isthe approximate probability that the total downtime for a period of30 days is less than 119 hours? (Round your answer to four decimalplaces.)

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