(b) "E(X)=pn=0.2*13=2.6"
The most likely outcome satisfies following inequality.
"np-q \\leq k \\leq np+p"
"13 \\cdot 0.2-0.8 \\leq k \\leq 13 \\cdot 0.2+0.2"
"1.8 \\leq k \\leq 2.8"
Thus, most likely, 2 elderly residents will welcome Mary’s visit.
The corresponding probability: "P(X=2)=C_{13}^2(0.2)^2(1-0.2)^{11}=0.2680"
(c) "Y=30X+5(13-X)=25X+65"
(i) "Y_{min}=25*0+65=65\\;min"
(ii) "Y_{max}=25*13+65=390\\;min"
(iii) "Y_{exp}=25*2.6+65=130\\;min"
(d) "W=100x+30(13-x)=70X+390"
(i) "W_{min}=70*0+390=390"
(ii) "W_{max}=70*13+390=1300"
(iii) "W_{exp}=70*2.6+390=572"
Comments
Leave a comment