Here are the solutions ...
(a)
Standard error of the mean is SE = σ/√n = 15/√60
For 95% confidence, the critical Z- score is 1.95996398454005
Width of the confidence interval is E = z * SE = 1.95996398454005 * 1.93649167310371 = 3.79545393564498
The confidence interval is [x-bar - E, x-bar + E]
= [80 - 3.79545393564498, 80 + 3.79545393564498]
= [76.20, 83.80]
(b)
Standard error of the mean is SE = σ/√n = 15/√120
For 95% confidence, the critical Z- score is 1.95996398454005
Width of the confidence interval is E = z * SE = 1.95996398454005 * 1.36930639376292 = 2.68379121557574
The confidence interval is [x-bar - E, x-bar + E]
= [80 - 2.68379121557574, 80 + 2.68379121557574]
= [77.32, 82.68]
(c)
As the sample size increases, the confidence interval narrows down.
