Answer
$P(between~7~and~12~inclusive)=0.878$
Work Step by Step
$P(between~7~and~12~inclusive)=P(7\leq X\leq12)=P(7)+P(8)+P(9)+P(10)+P(11)+P(12)={}_{15}C_{7}\times0.6^7\times0.4^{8}+{}_{15}C_{8}\times0.6^8\times0.4^{7}+{}_{15}C_{9}\times0.6^9\times0.4^{6}+{}_{15}C_{10}\times0.6^{10}\times0.4^{5}+{}_{15}C_{11}\times0.6^{11}\times0.4^{4}+{}_{15}C_{12}\times0.6^{12}\times0.4^{3}=6435\times0.6^7\times0.4^{8}+6435\times0.6^8\times0.4^{7}+5005\times0.6^9\times0.4^{6}+3003\times0.6^{10}\times0.4^{5}+1365\times0.6^{11}\times0.4^{4}+455\times0.6^{12}\times0.4^{3}=0.878$
