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Q: How do you calculate probability given mean and standard deviation?

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Square the standard deviation and you will have the variance.

49.30179172 is the standard deviation and 52 is the mean.

In order to answer this question, you will need to provide the standard deviation.

The Poisson distribution is a discrete distribution, with random variable k, related to the number events. The discrete probability function (probability mass function) is given as: f(k; L) where L (lambda) is the mean and square root of lambda is the standard deviation, as given in the link below: http://en.wikipedia.org/wiki/Poisson_distribution

A single number, such as 478912, always has a standard deviation of 0.

3.6

You need the mean and standard deviation in order to calculate the z-score. Neither are given.

A single number, such as 478912, always has a standard deviation of 0.

Yes.

Standard deviations are measures of data distributions. Therefore, a single number cannot have meaningful standard deviation.

It depends what you're asking. The question is extremely unclear. Accuracy of what exactly? Even in the realm of statistics an entire book could be written to address such an ambiguous question (to answer a myriad of possible questions). If you simply are asking what the relationship between the probability that something will occur given the know distribution of outcomes (such as a normal distribution), the mean of that that distribution, and the the standard deviation, then the standard deviation as a represents the spread of the curve of probability. This means that if you had a cure where 0 was the mean, and 3 was the standard deviation, the likelihood of observing a value of 12 (or -12) would be likely inaccurate if that was your prediction. However, if you had a mean of 0 and a standard deviation of 100, the likelihood of observing of a 12 (or -12) would be quite likely. This is simply because the standard deviation provides a simple representation of the horizontal spread of probability on the x-axis.

Assuming the returns are nomally distributed, the probability is 0.1575.

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