Re: Probability question that stumped me completely - reward
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Asked of me in an interview today and I couldn't figure it out at all. Given a series that is normally distributed with mean 0 and standard deviation of 1, what is the probability that the next 100 elements will have an average greater than 1.5?
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thylacine has it right. The average would have to be at least 15 standard deviations above the mean to be 1.5 or greater. This has a probability of zero for all practical purposes. I cannot even evaluate a probability this small in Excel.
This is a standard statistical problem. I would not make matters worse by telling your interviewer that it was "tricky". Even if you didn't know the distribution of the sample mean offhand, you should have been able to reason that an average of 1.5 would require that the sum of 100 elements be 150, and the standard deviation of the total is sqrt(100) = 10, so again we must be 15 standard deviations above the mean. This assumes you know that the distribution of the sample mean is normal if the original distribution is normal.
Why do you use the word "series"? I assume by this that you just mean a random variable, and the "elements" are just values of the random variable, or samples.
This also should have been posted in the probability forum.
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