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    Compute a probability by using the z-table

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    Fluctuation in the prices of precious metals such as gold have been empirically shown to be well approximated by a normal distribution when observed over short interval of time. In May 1995, the daily price of gold (1 troy ounce) was believed to have a mean of $383 and a standard deviation of $12. A broker, working under these assumptions, wanted to find the probability that the price of gold the next day would be between $394 and $399 per troy ounce. In this eventuality, the broker had an order from a client to sell the gold in the client's portfolio. What is the probability that the client's gold will be sold the next day?

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    Solution. Denote by X the daily price of gold (1 troy ounce). Then X follows a normal distribution with mean mu=$383 and standard deviation sigma=$12. So, the probability that the client's gold will be sold the next day is

    P[393<=X<=399] ...

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