Noah was lacking in belief, taught the 3rd century teacher, Rabbi Yohanan. If not for the water reaching his ankles, he would not have entered the ark.
Lacking in belief? Noah, who fulfilled the twin tasks of building the great ark and gathering its passengers? Rabbi Yohanan pressed his extraordinary claim through the verse: Noah… went into the ark because of the flood water (Genesis 7:7).
The verse itself does not shout Noah’s lack of faith. True, an earlier verse (Genesis 7:1) related that God’s command to enter the ark came before the rain began, helping to make the case that Noah hesitated. But hesitation is not the same as lack of belief. Something more compelling than the Torah text demanded the sage’s conclusion; namely, that these verses pointed to a deep human characteristic. Despite any indications, just like Noah, we sometimes simply refuse to believe that a thing will happen—until it does.
800 years later in northern France, Rashi elaborated Rabbi Yohanan’s teaching. Said Rashi: Noah, also, was among those people who are lacking in faith. He believed, and he did not believe, that the flood would come; so, he would not enter the ark until the water forced him.
For 800 years—from Rabbi Yohanan to Rashi—there is no evidence that any other teacher saw in the Noah story the Torah’s timeless assurance that contemporary souls are not alone in the tangle of belief.
To believe and—at the same time—not believe is unprecedented language unique to Rashi describing a human condition that is not unique at all. The Torah whispers it, but the compassionate teacher shouts it; assuring fellow-travelers that they are not alone in a world where floods threaten and believing is complicated.
Sicha - Continuing the Conversation 
A disciple of Rabbi Yechiel Michel of Zlotchov [1725-1785] asked him: “Since Noah went into the ark ‘because of the waters of the flood,’ Rashi interprets that Noah had small faith. He believed, and yet he did not believe, the word of God until the waters of the flood compelled him and only then did he enter the ark. How then was he righteous?” Rabbi Yehiel replied: “There are two types of faith: simple faith, which accepts the word and waits to see it fulfilled, and working faith, whose power contributes to the fulfillment of that which is to be. With all his heart Noah feared to believe in the coming of the flood, so that his faith might not make that coming more sure. And so he believed and did not believe, until the waters compelled him.”
“There are two types of faith: simple faith, which accepts the word and waits to see it fulfilled, and working faith, whose power contributes to the fulfillment of that which is to be.” There are 2 types of Cubs fans as to faith in the quasi-messianic expectation that the Cubs would — some day — win the World Series: Simple faith type read the scores the next day — smiling or frowning in response to wins, losses. Working faith type bought tickets or had friends with a roof in the neighborhood and showed up “faith-fully” at every home game. Cheered, bought and wore proudly caps, shirts. Attending via radio or tv earned half credit.
Traveling to attend away-games earned a chelek in the Olam Haba!
Seems to me that if we qualify “ani ma’amin” with “b’emunah shleimah,” the implication is that we could absolutely ma’amin in a state that ISN’T shleimah…
Davar acheir: the words “aseh l’cha teyva….” are usually translated: “Make an ark FOR yourself.”
A midrash offers an alternative: “Make an ark OF yourself.” I preached on that text for my HUC Chapel Sermon in 1959. It went over so well that I continued to use it (the text) almost every year thereafter. (Wish I could find the source).