Answer:
a)Sample size would be required to obtain a margin of error of 1 days is
n = 179
b) sample size would be required to obtain a margin of error of 2.5 days is n = 20
Explanation:
step(i):-
Given Population standard deviation = 6.83 days
a) Given margin of error = 1 day
The margin of error is determined by

Step(ii):-
Given 95 % of confidence level
Now the critical value Z₀.₀₅ = 1.96

√n = 13.38
Squaring on both sides, we get
n = 179.206
b)
step(i):-
a) Given margin of error = 2.5 day
The margin of error is determined by

Step(ii):-
Given 90 % of confidence level
Now the critical value Z₀.₁₀ = 1.645

Cross multiplication , we get

√n = 4.494
Squaring on both sides, we get
n = 20.19
Final answer:-
a)Sample size would be required to obtain a margin of error of 1 days is
n = 179
b) sample size would be required to obtain a margin of error of 2.5 days is n = 20