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Lifts usually have signs indicating their maximum capacity. Consider a sign in a lift that reads "maximum capacity 1400kg or 20 persons". Suppose that the weights of lift-users are normally distributed with a mean of 65kg and a standard deviation of 10kg.
(a) What is the probability that a lift-user will weigh more than 70kg?
(b) What is the probability that a lift-user will weigh between 60 and 75kg?
(c) What is the probability that 20 people will exceed the weight limit of 1400kg?
(d) What is the probability that 25 people will not exceed the weight limit?
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