3. An elevator has weight capacity 3000 lb. Assume that the weight Xofa randomly

Question

3. An elevator has weight capacity 3000 lb. Assume that the weight Xofa randomly selected person has i 175, a 400. Let Wn be the total weight of n passengers a) Find a formula for E(Wn) and o2(W). b) If 18 people get on the elevator, what is the probability that the total weight of passengers exceeds the weight capacity of the elevator? c What is the maximum number Nof people allowed on the elevator such that the probability of their combined weight exceeding the 3000-lb load limit is less than 0.05?

Explanation / Answer

c)mean weight of N people =175N

and std deviation of N people =20*(N)1/2

here P(X>3000) <0.05

1-P(X<3000) <0.5

P(X<3000)>0.95

(3000-175N)/20N1/2 >1.6449

3000-175N>1.6449*20*(N)1/2

solving above by putting value of N from 10 onwards

the maximum value for whcih above holds true is N=16

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