Question

How are the 95% confidence interval, 68-95-99.7 rule, and standard error related?

Answer 1

68-95-99.7 rule also known as Empirical rule. According to this rule for approximately normally distributed data the values within one standard deviation of the mean are 68% of the data set; within two standard deviations of the mean is  95% of the data set; and within three standard deviations of the mean are 99.7%.of the data set.

So according to 68-95-99.7 rule 95% confidence interval are within two standard deviations of the mean.

Suppose we have a sample of size n and we want to know find 95% confidence interval for mean. In this case according to 68-95-99.7 rule we will use

the term is known as standard error . So that's how the 95% confidence interval, 68-95-99.7 rule, and standard error related.