A helicopter is allowed to carry at most 8 persons given that their total weight does not

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A helicopter is allowed to carry at most 8 persons given that their total weight does not exceed \(620 \mathrm{~kg}\). The weights of the passengers are independent, identically normally distributed random variables with mean value \(76 \mathrm{~kg}\) and variance \(324 \mathrm{~kg}^{2}\).

(1) What are the probabilities of exceeding the permissible load with 7 and 8 passengers, respectively?

(2) What would the maximum total permissible load have to be to ensure that with probability 0.99 the helicopter will be allowed to fly 8 passengers?

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