The number of people that get in an elevator for trips from the ground floor in

Question

The number of people that get in an elevator for trips from the ground floor in a tall office building is given by the probability distribution below.x p(x) 1 0.002 2 0.010 3 0.050 4 0.060 5 0.080 6 0.090 7 0.100 8 0.120 9 0.140 10 0.150 11 0.150 12 0.048 a) Find the mean, variance, and standard deviation of the number of people in a trip, using the formulas from the lecture slides. b) For a randomly selected trip, what is the probability of the number of riders being within one standard deviation of the mean? c) For two randomly selected trips, what is the probability that both trips have a number of riders more than two standard deviations from the mean?

Explanation / Answer

a) mean = E(X) = X1P(X1)+X2P(X2)+.....+XNP(XN)

1*0.002+2*0.010+3*0.050+4*0.060+5*0.080+6*0.090+7*0.100+8*0.120+9*0.140+10*0.150+11*0.150+12*0.048 = 7.998

VARIANCE = E(X^2) - E(X)^2

E(X^2) = 69.59

E(X) = 7.99

VAR(X) = 69.59 - 7.99 = 61.6

STANDARD DEV = 61.6^(1/2) = 7.84

B) WITHIN 1 STANDARD DEV = STANDARD DEV +1 AND STANDARD DEV -1 = (7,9)

P(7<X<9) = 0.100+0.120+.140 = 0.360

C) WITHIN TWO STANDARD DEV = STANDARD DEV +2 AND STANDARD DEV -2 = (6,10)

P(6<X<10) = 0.9+0.1+0.12+0.14+0.15 = 0.6

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