What is the probability that a normal variate takes a value greater than its mean?

What is the probability that a normal variate takes a value greater than its mean?

1/2 is the probability that a normal variate takes a value greater than its mean.

What is the standard normal probability distribution?

The standard normal distribution is a normal distribution with a mean of zero and standard deviation of 1. Examine the table and note that a “Z” score of 0.0 lists a probability of 0.50 or 50%, and a “Z” score of 1, meaning one standard deviation above the mean, lists a probability of 0.8413 or 84%.

How to calculate probabilities for normally distributed situations?

Given a situation that can be modeled using the normal distribution with a mean μ and standard deviation σ, we can calculate probabilities based on this data by standardizing the normal distribution. Note in the expression for the probability density that the exponential function involves .

Why is the normal distribution a continuous distribution?

Because the normal distribution is a continuous distribution, we can not calculate exact probability for an outcome, but instead we calculate a probability for a range of outcomes (for example the probability that a random variable X is greater than 10). The normal distribution is symmetric and centered on the mean (same as the median and mode).

How to calculate the probability of a range of values?

Finally, we might want to calculate the probability for a smaller range of values, P(a < X ≤ b). First, we calculate P(X ≤ b) and then subtract P(X ≤ a). The graph below helps illustrate this situation. Thus, we are able to calculate the probability for any range of values for a normal distribution using a standard distribution table.

What is the probability of a random variable taking on a value?

Thus, there is a 0.6826 probability that the random variable will take on a value within one standard deviation of the mean in a random experiment.