Let X= the number of of workers agree: X∼Bin(n,p)
P(X=x)=(xn)px(1−p)n−x Given n=18,p=0.58
i.
P(X≥5)=1−P(X<5)
=1−P(X=0)−P(X=1)−P(X=2)
−P(X=3)−P(X=4) P(X=0)≈1.65×10−7
P(X=1)≈4.11×10−6
P(X=2)=0.0000482543
P(X=3)=0.00035539679
P(X=4)=0.00184044764
P(X≥5)≈0.99775162498 ii.
P(4≤X≤12)=1−P(X<4)−P(X>12)
=1−0.00040792739−0.1628374012
=0.1628374012 iii.
P(X≤8)=0.176778472
iv.
mean=E(X)=np=18(0.58)=10.44
σ2=np(1−p)=18(0.58)(1−0.58)
=4.3848
σ=σ2=4.3848≈2.0940
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