Calculating Probabilities Using The Confidence Interval Formula

Confidence Intervals can be used to estimate the population mean from a sample mean and finding a confidence interval can be calculated by using this formula;

confidence interval formula

Symbol Property
x bar Mean of the sample
z value  Standard score
standard deviation squared (variance) Standard deviation squared (variance)
n Number in sample

The Standard Score can be calculated by taking one away from the probability dividing by two and then adding the probability back to the answer and using the table to calculate. So for example, a probability of 95% would be,

calculating z value of 95 percent probability for a confidence interval

Of which z value to point 975 is found by using percentage points of the normal distribution.

normal distribution table for 95 percent z value

Using a Confidence Interval of 95% would allow you to assume that you are 95% confident about your results and that there is supposedly a 5% area of doubt where the samples are uncertain, It is important to consider this factor when conducting a conclusive statement.