Muslims have the responsibility of conveying the message of Islam to others in order to be able to witness on the Day of Judgement!

Verses 77-78 of Chapter 22

O people, who have believed, bow down and prostrate yourselves before Allah, worship your Lord and do righteous deeds: it may be that you attain true success. Exert your utmost for the cause of Allah as one should. He has chosen you for His service and has not laid on you any hardship in your religion. Therefore, be steadfast in the religion of your father Abraham. Allah had called you "Muslims" before this and has called you (by the same name) in this (Qur'an) also so that the Messenger may be a witness in regard to you and you may be witnesses in regard to the rest of mankind. Therefore, establish Salat and pay the Zakat dues, and hold fast to Allah, for He is your Guardian: What an excellent Guardian and what an excellent Helper!