what do you mean by standard deviation of 95%
Recall that with a normal distribution, 95% of the distribution is within 1.96 standard deviations of the mean. Using the t distribution, if you have a sample size of only 5, 95% of the area is within 2.78 standard deviations of the mean.Therefore, the standard error of the mean would be multiplied by 2.78 rather than 1.96. The values of t to be used in a confidence interval can be looked up in a table of the t distribution.he value of 1.96 is based on the fact that 95% of the area of a normal distribution is within 1.96 standard deviations of the mean; 12 is the standard error of the mean. Figure 1. The sampling distribution of the mean for N=9. The middle 95% of the distribution is shaded.