Answer :
Answer:
a) P = 0.591
b) P = 0.0000358
c) 11 inmates
Step-by-step explanation:
This is a binomial distribution exercise.
Where p = 0.55 is the success probability
The random variable is X : ''number of inmates serving time for drug dealing''
X ~ Bi(n;p)
Where n is the random sample and p is the success probability
The probability function is :
[tex]P(X=x)=f(x)=nCx.p^{x}.(1-p)^{n-x}[/tex]
Where nCx is the combinatorial number define as
[tex]nCx=\frac{n!}{x!(n-x)!}[/tex]
a) [tex]P(X\geq 11) =f(11)+f(12)+f(13)+f(14)+f(15)+f(16)+f(17)+f(18)+f(19)+f(20)[/tex]
[tex]P(X\geq 11)=0.1771+0.1623+0.1221+0.0746+0.0365+0.0139+0.004+0.0008+0.0001+0.55^{20}[/tex]
[tex]P(X\geq 11)=0.591[/tex]
b)
[tex]P(X\leq 2)=f(0)+f(1)+f(2)=0.0000358[/tex]
c) The expected number for X is
[tex]np=20(0.55)=11[/tex]