Finding the minimum # of items to be sold to meet a goal, based on likelihood
Let's start with an environment in which there is only ever a single pledge level. The question at hand is: how do we choose the dollar amount of that level to maximise revenue (income)?

Observation 1: your probability distribution implies a demand curve.

We can plot the cumulative distribution of willingness to pledge and it will probably look roughly like this (with most of the mass at the bottom, as you speculate):



The $y$ value in this figure tells us the probability that a given individual's willingness to pledge (WTP) is no greater than the dollar value on the $x$ axis.

By turning this upside down, we get the probability that somone is willing to pay at least this much:



This tells us, for example, that there is a rouly 55% chance of a randomly selected individual being willing to pledge at least \$10. If we take 100 people then, on average, 55 of them will pledge. Thus, we can think of the vertical axis as being an indirect way of measuring pledge quantities, corresponding with the pledge level (or price) on the horizontal axis. If we swap the two axes, we therefore get something that looks very much like a textbook demand curve:



Given this demand curve, we can use all of the usual tools from the kind of standard monopoly optimisation problem that you can find in and introductory economics textbook. For example, if the CDF in the first figure is given by function $F$ then$$\Pr(\text{WTP}&gt;x)=1-F(x)$$ so the revenue from setting the pledge level at $x$ when the audience consists of $n$ potential pledgers is $R(x)=[1-F(x)]xn$. Just like a standard monopolist's problem, we can compute the revenue-maximizing pledge level ("price") by setting marginal revenue equal to zero:

$$R'(x)=n[1-F(x)]-xnF'(x)=0.$$

Substituting your empirical distribution for $F$ in this equation and solving for $x$ gives your optimal pledge level.



Now, if we allow for multiple pledge levels then things become much more complicated. Firstly, we need a model of the behaviour of people and why it is that some people might pledge more than others.

If, for example, we are working in a Kickstarter-like environment then the main motive would be to get the goodies that come with the higher pledge tier. But that means we need a model not only of the pledge levels, but what you get in return. A complete treatment of this is beyond the scope of this answer, but a fairly readable summary can be found in "Versioning Information Goods" by Hal Varian. If you want a more detailed, technical treatment then the best place to look is "The Economics of Contracts: A Primer" by Salanie.