$\text{The Sampling Distribution of } \overline{Y}$
$\text{Samples } N$
100
200
300
400
500
600
700
800
900
1,000
1,000
$\text{Sample Size } n$
100
200
300
400
500
600
700
800
900
1,000
100
$ Y \sim \mathcal{N} (5,25^2) $
$ \widehat{\sigma} = 2.4679$
$ \frac{1}{N}\sum_{i\in N} \overline{Y}_i = 5.0118$
$\text{standardize as }\frac{\overline{Y}_i - 5}{25}$
$\text{also scale by }\sqrt{n}$
4
21
77
154
204
215
172
94
44
12
3
-2.40
-0.98
0.45
1.87
3.30
4.72
6.15
7.57
8.99
10.42
11.84
-3.83
13.27
14.69