# Question

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?

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