Using the binomial distribution:
[tex]P(X\le x)=\frac{n!}{k!(n-k)!}p^k(1-p)^{n-k}[/tex]
a.
[tex]\begin{gathered} p=0.55 \\ n=37 \\ P(X=20)\approx0.1298 \end{gathered}[/tex]
b.
[tex]P(x\le21)\approx0.6460[/tex]
c.
[tex]P(X\ge19)\approx0.7303[/tex]
d.
[tex]P(17\le X\le21)\approx P(X\le21)-P(X<17)\approx0.5440[/tex]
