Answer: The number of first-year residents she must survey to be 95% confident= 263
Step-by-step explanation:
When population standard deviation ([tex]\sigma[/tex]) is known and margin of error(E) is given, then the minimum sample size (n) is given by :-
[tex]n=(\dfrac{z^*\sigma}{E})^2[/tex], z* = Two-tailed critical value for the given confidence interval.
For 95% confidence level , z* = 1.96
As, [tex]\sigma[/tex] = 8.265, E = 1
So, [tex]n= (\dfrac{1.96\times8.265}{1})^2 =(16.1994)^2\\\\= 262.42056036\approx263\ \ \ [\text{Rounded to the next integer}][/tex]
Hence, the number of first-year residents she must survey to be 95% confident= 263
