Question

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)=?

Answer 1

Please don't hesitate to give a "thumbs up" for the answer in case the answer has helped you

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