Probability of selling a stock higher than you bought it

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To determine the probability of selling Apple Inc. stock at or above the purchase price of $300 after 10 years, the Gaussian distribution can be applied. The average daily stock price is $297 with a variance of $5, allowing for calculations of probabilities using the normal distribution. Instead of calculating probabilities for each individual price point, a normal distribution table can provide the probability for values greater than $300 directly. The historical data indicates that the duration of stock ownership does not affect the calculation. This approach simplifies the analysis of potential future stock prices.
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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?


Homework Equations





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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