Question

# 16% adults favor the use of unmanned drones by police agencies. Twelve U.S. adults are randomly...

16% adults favor the use of unmanned drones by police agencies. Twelve U.S. adults are randomly selected. Find the probability that the number of U.S. adults who favor the use of unmanned drones by police agencies is​ (a) exactly​ three, (b) at least​ four, (c) less than eight

(a)P(3)=?

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This is an application of binomial distribution.

a. P(X=3) = ?
So, p(right) = p = .16
Using this in P(x,n,p) = nCx*p^x*(1-p)^(n-x)
P(3,12,.16)
= 12C3*.16^3*.84^9
= 0.1876

b. P(X>=4)
= 1-P(X<=3)
= 1-( P(X=0)+P(X=1)+P(X=2)+P(X=3))
= 1-(12C0*.16^0*.84^12+12C1*.16^1*.84^11+12C2*.16^2*.84^10+12C3*.16^3*.84^9)
= 1- 0.8886
= 0.1114

c. P(X<8)
= P(X<=7)
= P(X=0)+..+P(X=7)
= 12C0*.16^0*.84^12 +....+ 12C7*.16^7*.84^5
= 0.405491009 +..+0.000889122
= 0.9999

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