Do familiar connections/alumni really help you gain access to top tier law schools?

My grandfather graduated from UPenn and the UPenn Dental School. My mother also attended UPenn but dropped out in her senior year. I am currently studying for the LSAT's and was wondering what type of advantage this connection might have for me. A little background on me, I graduated from the University of South Florida with a degree in Political Science and a 3.4 GPA. I was hoping to get a score in the mid 160's. Any advice/info would be greatly appreciated.