Answer
a) $p(X\leq 3)=0.4114$
b) $p(X\gt 10)=0.0006$
c) $p(X=6)=0.1091$
d) $p(6\leq x\leq11)=0.1957$
Work Step by Step
Given that, n=20, P=0.2, from the binomial table II in Appendix A which contain the cumulative probabilities $p(X\leq x)$
a) $p(X\leq 3)=0.4114$ (the row with n=20, x=3 and the column of p=0.2)
b) $p(X\gt 10)=1-p(X\leq 10)=1-0.9994=0.0006$ (the row with n=20, x=10 and the column of p=0.2)
c) $p(X=6)=p(X\leq 6)-p(X\leq 5)=0.9133-0.8042=0.1091$ (the row with n=20, x=6 , x=5 and the column of p=0.2)
d) $p(6\leq x\leq11)=p(X\leq 11)-p(X\leq 5)=0.9999-0.8042=0.1957$
(the row with n=20, x=11 , x=5 and the column of p=0.2)
