Let X= the number of patients survived: X∼Bin(n,p).
Given p=0.4,n=10.
q=1−p=1−0.4=0.6
i.
P(X≥6)=P(X=6)+P(X=7)+P(X=8)
+P(X=9)+P(X=10)
=(610)(0.4)6(0.6)10−6+(710)(0.4)6(0.6)10−7
+(810)(0.4)8(0.6)10−8+(910)(0.4)9(0.6)10−9
+(1010)(0.4)10(0.6)10−10=0.1662386176
ii.
P(2≤X≤7)=P(X=2)+P(X=3)
+P(X=4)+P(X=5)+P(X=6)+P(X=7)
=(210)(0.4)2(0.6)10−2+(310)(0.4)3(0.6)10−3
+(410)(0.4)4(0.6)10−4+(510)(0.4)5(0.6)10−5
+(610)(0.4)6(0.6)10−6+(710)(0.4)7(0.6)10−7=0.9413480448
iii.
P(X=3)=(310)(0.4)3(0.6)10−3
=0.214990848 iv.
P(X=10−2)=(810)(0.4)8(0.6)10−8
=0.010616832
v.
E(X)=np=10(0.4)=4
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