Problem:
A helicopter is allowed to carry at most 8 persons provided that their total weight does not exceed 620kg. The weights of the passengers are independent, identically normally distributed random variables with mean value and standard 76 kg deviation 18kg.
(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?