If you had known average and standard deviation of sample which size is N, you could estimate the range of population average with 95 % probability. In standard normal distribution, sum of area under curve greater than 1.96 and less than – 1.96 is 0.05. There is population average between exception multiplying 1.96 by standard error from average and sum of the multiplied and average, called as 95 % confidence interval (95 % CI).
