SOLUTION: Given the following values: 2.3 3.6 4.8 5.5 6.1 6.2 6.8 7.2 7.7 8.0 8.3 8.5 8.9 9.1 9.6 10.2 10.4 11.2 11.4 11.7 11.8 12.1 12.3 13.5 14.5 15.3 15.9 16.6

Question 1048067: Given the following values:
2.3
3.6
4.8
5.5
6.1
6.2
6.8
7.2
7.7
8.0
8.3
8.5
8.9
9.1
9.6
10.2
10.4
11.2
11.4
11.7
11.8
12.1
12.3
13.5
14.5
15.3
15.9
16.6
18.7
19.5
What is the proportion of video duration that are longer than 8 minutes? What is the proportion of durations that lie within one standard deviation of the mean? What is the proportion of durations that lie within two standard deviations of the mean? Is this proportion consistent with the empirical rule?

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
There were 30, and 21 or 70% were longer than 8 minutes (strictly speaking 20 were, since the 21st was 8 minutes exactly). That would be 2/3s.
The mean is 10.26 with sd 4.29 (treated as a sample, dividing by 29).
Within 1 sd is (5.97,14.55) are 21 or 70%, certainly consistent with the empirical rule.
Within 2 sd is (1.68,18.84) are 29/30 or 96.7%, again consistent with the empirical rule.
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