Question

3. What is the width of 68% confidence interval in terms of standard deviation (How many standard deviation is equivalent to the width of 68% confidence interval)?

What about 95% and 99.7%?

Answer 1

3.The width of 68% confidence interval in terms of standard deviation is 1.

Empirical rule shows that

1.68% falls within the first standard deviation (µ ± σ),

2.95% within the first two standard deviations (µ ± 2σ)

3.99.7% within the first three standard deviations (µ ± 3σ).

68% confidence interval = ( - ) X ( + ) ​​ =  ( + ) ​​ - ( - ) = 2

95% confidence interval = ( - 2) X ( +2 ) ​​ =  ( +2 ) ​​ - ( -2 ) = 4

99.7% confidence interval = ( - 3) X ( +3 ) ​​ =  ( +3 ) ​​ - ( -3 ) = 6