Answer
$E(X)=4.32$ rooms.
Work Step by Step
$E(X)=μ_X=Σ[x.P(x)]=1\times P(1)+2\times P(2)+3\times P(3)+4\times P(4)+5\times P(5)+6\times P(6)+7\times P(7)+8\times P(8)+9\times P(9)]=1\times0.011+2\times0.028+3\times0.228+4\times0.337+5\times0.233+6\times0.108+7\times0.037+8\times0.013+9\times0.005=4.32$
