The answer depends on the underlying distribution. For example, if you have a random variable X, with a symmetric distribution with mean = 20 and sd = 1, then
prob(X > 1) = 1, to at least 10 decimal places.
a mean of 1 and any standard deviation
Intuitively, a standard deviation is a change from the expected value.For the question you asked, this means that the change in the "results" doesn't exist, which doesn't really happen. If the standard deviation is 0, then it's impossible to perform the test! This shows that it's impossible to compute the probability with the "null" standard deviation from this form:z = (x - µ)/σIf σ = 0, then the probability doesn't exist.
probability is 43.3%
a is true.
The standard deviation is the standard deviation! Its calculation requires no assumption.
with mean of and standard deviation of 1.
The mean and standard deviation do not, by themselves, provide enough information to calculate probability. You also need to know the distribution of the variable in question.
a mean of 1 and any standard deviation
with mean and standard deviation . Once standardized, , the test statistic follows Standard Normal Probability Distribution.
no
Assuming the returns are nomally distributed, the probability is 0.1575.
Intuitively, a standard deviation is a change from the expected value.For the question you asked, this means that the change in the "results" doesn't exist, which doesn't really happen. If the standard deviation is 0, then it's impossible to perform the test! This shows that it's impossible to compute the probability with the "null" standard deviation from this form:z = (x - µ)/σIf σ = 0, then the probability doesn't exist.
probability is 43.3%
The probability is 0.5
a is true.
The probability of an event occurring within 5 standard deviations from the mean is extremely rare, as it falls outside the normal range of outcomes.
The mean deviation (also called the mean absolute deviation) is the mean of the absolute deviations of a set of data about the data's mean. The standard deviation sigma of a probability distribution is defined as the square root of the variance sigma^2,