$\text{The Sampling Distribution of } \overline{Y}$
$\text{Samples } N$
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} = 2.5787$
$ \frac{1}{N}\sum_{i\in N} \overline{Y}_i = 4.8714$
$\text{standardize as }\frac{\overline{Y}_i - 5}{25}$
$\text{also scale by }\sqrt{n}$
6
14
74
131
191
225
179
111
42
22
5
-2.93
-1.48
-0.03
1.42
2.86
4.31
5.76
7.21
8.66
10.11
11.56
-4.38
13.01
14.45