Which female musician is known for her hits "All About That Bass" and "Lips Are Movin'"?

 The female musician known for her hits "All About That Bass" and "Lips Are Movin'" is Meghan Trainor. 

Both songs were released in 2014, with "All About That Bass" becoming a massive commercial success and topping the charts in multiple countries. 

Meghan Trainor's catchy pop melodies and body-positive lyrics have earned her widespread popularity and acclaim in the music industry.