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

The downtime per day for a computing facility has mean 4 hours and standard deviation 0.9 hour. (a) Suppose that we want to compute probabilities about the average daily downtime for a period of 30 days. (i) What assumptions must be true to use the result of the central limit theorem to obtain a valid approximation for probabilities about the average daily downtime? (Select all that apply.) The daily downtimes must have an approximately normal distribution. The number of daily downtimes must be greater than 30. The daily downtimes must have an expected value greater than their variance. The daily downtimes must have the same expected value and variance. The daily downtimes must be independent and identically distributed random variables. (ii) Under the assumptions described in part (i), what is the approximate probability that the average daily downtime for a period of 30 days is between 1 and 5 hours? (Round your answer to four decimal places.) (b) Under the assumptions described in part (a), what is the approximate probability that the total downtime for a period of 30 days is less than 119 hours? (Round your answer to four decimal places.)

Expert Solution

Answer :-

Given that

The mean () = 4

The standard deviation () = 0.9

Colby Messinger answered 2 years ago

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