Answer:
(a) 0.8655
(b)0.8655
Step-by-step explanation:
X is the number of respodents who agree
P(x ≥4), n=12, p=0.45
P(x ≥4)=1-P(x<4)
P(x<4)=P(0 ≤x<4)= P(0 ≤x≤3)=P(x=0,1,2,3)=P(x=0)+P(x=1)+P(x=2)+P(x=3)
[tex]P(x=0)=12C0(0.45)^{0}(1-0.45)^{12-0}\approx 0.0007662[/tex]
[tex]P(x=1)=12C1(0.45)^{1}(1-0.45)^{12-1}\approx 0.007523[/tex]
[tex]P(x=2)=12C2(0.45)^{2}(1-0.45)^{12-2}\approx 0.033853[/tex]
[tex]P(x=3)=12C3(0.45)^{0}(1-0.45)^{12-3}\approx 0.092326[/tex]
[tex]P(x<4)= 0.0007662+0.007523+0.033853+0.092326=0.134468[/tex]
P(x ≥4)=1-P(x<4)=1-0.134468=0.8655319
(b)
Y represent those who agree
P(Y≤8), n=12, p=0.45
P(Y≤8)=1-P(Y>8)
P(Y>8)=P(8<Y≤12)=P(9≤Y≤12)=P(Y=9,10,11,12)
[tex]P(Y=9)= 12C9(0.45)^{9}(1-0.45)^{12-9}\approx 0.092326[/tex]
[tex]P(Y=10)= 12C10(0.45)^{10}(1-0.45)^{12-10}\approx 0.033853[/tex]
[tex]P(Y=11)= 12C11(0.45)^{11}(1-0.45)^{12-11}\approx 0.007523[/tex]
[tex]P(Y=12)= 12C12(0.45)^{12}(1-0.45)^{12-12}\approx 0.0007662[/tex]
Total =0.134468
P=1-0.134468=0.8655319
