The Cyprus Amax Minerals Company signed a deal yesterday with underwriters to sell its stake in the Kinross Gold Corporation of Toronto to the public for $4 (Canadian) a share. In United States dollars, the shares will be sold for about $2.71 each, for proceeds of about $242 million. Cyprus said it and its affiliates have agreed to sell their total holding of 89 million Kinross shares. Cyprus Amax, based in Englewood, Colo., said it would realize net proceeds of $232 million.