Probability of selling a stock higher than you bought it

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SUMMARY

The discussion focuses on calculating the probability of selling Apple Inc. stock at or above the purchase price of $300 after 10 years, given an average daily stock price of $297 and a variance of $5. The primary method suggested for solving this problem is through Gaussian distribution, which allows for direct calculation of probabilities without needing to evaluate each price increment separately. The relevance of the 10-year holding period is deemed negligible since the calculation is based on historical averages.

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Homework Statement


I buy a stock at Apple Inc. History shows that the average daily stock price is $297 with a variance of $5. If I buy a stock at $300, what is the probability that after 10 years I will be able to sell the stock at at least that price?


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The Attempt at a Solution



I know of one way to solve this problem: Gaussian distribution. I know that I can calculate the probability of $300, $301, $302,...$n with a simple equation. I just want to know if there is another way of doing it.
 
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Yes, use Gaussian distribution. But why calcuate "$300, $301, $302, ..." separately? Any good table of the normal distribution will give you the probability that "x> 300" directly. What did you get for the "standard normal" variable for x= 300?

(Since you are using the "historic" values, the "10 years" you owned the stock is irrelevant.)
 

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