Edward^1 Norrice immigrated 1639 as per Anderson, The Great Migration Directory, see AmericanAncestors.
Edward^2 Norris immigrated, perhaps with his father in 1639; he was first noticed in the Salem Town Records, 21 January 1639/40, "Yong mr. Norris Chose by this assemblie to teach skoole."
Mary^2 Norris immigrated earlier, 1635, and is first noticed in that year's Roxbury Church records. "Mary Norrice a maide. She came into the Land. She was daughter to Mr Edward Norrice, who came in to the land [blank] & was called & ordained to be Teacher to the Church at Salem where he served the Lord Christ." See also Robert Charles Anderson, The Great Migration, Immigrants to New England, 1634-1635, Volume V, M-P (2007), 266-67 (Mary Norris); digital images by subscription, AmericanAncestors.
I am still working on these profiles, but believe enough has been entered to show that they qualify.