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
1.10
(78-259)/229.1= -.79
No. Standard deviation is not an absolute value. The standard deviation is often written as a single positive value (magnitude), but it is really a binomial, and it equals both the positive and negative of the given magnitude. For example, if you are told that for a population the SD is 5.0, it really means +5.0 and -5.0 from the population mean. It defines a region within the distribution, starting at the lower magnitude (-5.0) increasing to zero (the mean), and another region starting at zero (the mean) and increasing up to the upper magnitude (+5.0). Both regions together define the (continuous) region of standard deviation from the mean value.
The answer depends on the distribution of the random variable. For some variables it is easy to calculate the cumulative distribution, F(x).Then, the probability between the values p and q is F(q) - F(p). WARNING: This might need minor modification if the the distribution is discrete.The normal distribution is one which, in general, cannot be evaluated analytically. However, you can convert p and q to the x=corresponding z-score. If m is the mean and s the standard deviations, then z1 = (p - m)/s and z2 = (q - m)/s. The cumulative probability function for Z is tabulated (widely available online) and the probability between p and q is F(z2) - F(z1).Note, however, that sometimes the tabulated values are (Prob - 0.5), or are 1 - Prob(z) so read notes to the table.
Square the standard deviation and you will have the variance.
49.30179172 is the standard deviation and 52 is the mean.
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
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.
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.
A single number, such as 478912, always has a standard deviation of 0.
Assuming the returns are nomally distributed, the probability is 0.1575.
Yes.
Standard deviations are measures of data distributions. Therefore, a single number cannot have meaningful standard deviation.
The probability of a phone being answered in 2 minutes, given that the average time is 3 minutes, is not specified in the information given. More details or specific probabilities are needed to determine the answer.