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1. Smallest average of distinct even integers ●○○○○ 10 ptsWhat is the smallest possible average of four distinct positive even integers?
2. Smallest maximum rounding error ●●○○○ 20 ptsThe sum of the following seven numbers is exactly 19: $a_1 = 2.56,$ $a_2 = 2.61,$ $a_3 = 2.65,$ $a_4 = 2.71,$ $a_5 = 2.79,$ $a_6 = 2.82,$ $a_7 = 2.86.$ Each $a_i$ is approximated by an integer $A_i,$ for $1 \le i \le 7,$ such that the sum of the $A_i$'s is also $19.$ Let $M$ be the maximum of the seven errors $|A_i - a_i|.$ What is the smallest possible value of $M$? Give your answer as a decimal.