Question

A very large data set (N > 10,000) has a mean value of 1.47 units and a standard deviation of 0.035 units. Determine the range of values in which 95% of the data set should be found assuming normal probability density (find a in the equation xi = x' ± a).

Answer 1

Using the 68 - 95 - 99.7 rule, 95% of the data set values will lie in the range of $(\mu - 2\sigma, \mu + 2\sigma)$ .

Hence, the range is = (1.47 - (2 * 0.035), 1.47 + (2 * 0.035)) = (1.40, 1.54).

(Here, a = $2\sigma$ = 2 * 0.035 = 0.07.)