First, the problem as you have presented it is odd. In reality, investments come with a price. On the assumption that you know the distribution of each payoff’s distribution, you would take differences in price into account. That is, if one of the 35 investments has a current price of 3 and the other has a current price of 30, most people would prefer to buy the chance to get somewhere between 35 - 33 = 2 and 35 + 33 = 58 for 3, where you are almost guaranteed to make a profit, than at 30, where there is a decent probability that you will incur a loss. A problem on selection of investments where the price of the different investments is unknown but the distribution of possible future returns is known is a problem so far removed from reality that I have trouble treating it seriously.
in practice, price is known with certainty and the distribution of future returns is unknown. I once was offered an investment in exploiting a used oil well using a new technique to recover residual oil. I was given a table of oil recovered by that technique at different abandoned wells. That provided a solid basis for creating a distribution of physical returns. But monetary returns also depended on future oil prices averaged over many months. The best that could be done was to create a probability distribution that was plausible.
Second, you can attack this problem on the assumption that the prices are equal. Now if you can only buy one, you would almost certainly buy one of the 35 return investments because the expected return is higher. If you can buy more than one, you would want to look at covariances among the investments. It will almost certainly be the case that a combination of the investments will generate an expected value with less variance.
Ceteris paribus, higher expected return is better, and, for most people, lower variance is better. The practical problem is that in most cases everything is not the same and neither the expected value nor the variance is better than an educated guess.
