It has been suggested that an investment portfolio selected randomly by throwing darts at the stock market page of The Wall Street Journal may be a sound (and certainly well-diversified) investment.
Suppose that you own such a portfolio of 16 stocks randomly selected from all stocks listed on the New York Stock Exchange (NYSE).
On a certain day, you hear on the news that the average stock on the NYSE rose 1.5 points.
Assuming that the standard deviation of stock price movements that day was 2 points and assuming stock price movements were normally distributed around their mean of 1.5, what is the probability that the average stock price of your portfolio increased?