Question: Problem 6.9 An elevator has a weight capacity of 3000 lbs. Assume that the weight X of a randomly selected person is N(175, 400) distributed,

Problem 6.9 An elevator has a weight capacity of 3000 lbs. Assume that the weight X of a randomly selected person is N(175, 400) distributed, i.e., µ = 175, σ = 20. Let Wn denote the total weight of n passengers.

(a) Give the formulas for: E(Wn) and V (Wn).

(b) Describe the distribution of Wn.

(c) If 18 people get on the elevator what is the probability that the total weight of the pas[1]sengers exceeds the weight capacity of the elevator?

(d) What is the maximum number N of persons allowed on the elevator so that the proba[1]bility of their combined weight exceeding the 3, 000 lb load limit is less than 0.05?

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