By dividing the observations with σ and by subtracting the mean of the distribution, we can transform any normal distribution into the standard one with mean 0 and standard deviation of one. In this case, this means that we need to find the confidence interval of (-2,88, 2,88) for the standard normal distribution. We can look this up in a standard table; The probability that an observation is below -2,88 is 0,002 and the probability that it is below 2,88 is 0,998. Hence, we have that 0,996 of the observations is in this interval, thus 99,6% is the confidence level of the given interval.
