Answer
a. $0.008$
b. 0.724
c. $0.00021$
d. 0.275
Work Step by Step
Use the binomial formula: $P(x)=_nC_x\cdot p^x(1-p)^{n-x}$ or the table in the appendix:
a. P(X = 8)=$_{12}C_8\times 0.3^8\times0.7^4=0.008$
b. P(X < 5)=P(X=0,1,2,3,4)=P(0)+P(1)+P(2)+P(3)+P(4)=0.014+0.071+0.168+0.240+0.231=0.724
c. P(X $\geq$ 10)=P(10)+P(11)+P(12)
=$_{12}C_{10}\times 0.3^{10}\times0.7^2+_{12}C_{11}\times 0.3^{11}\times0.7+_{12}C_{12}\times 0.3^{12}\times0.7^0=0.00021$
d. P(4 < X $\leq$ 9)=P(5)+P(6)+P(7)+P(8)+P(9)=0.158+0.079+0.029+0.008+0.001=0.275