Answer: 74.5% of the measurements fall within one standard deviation of the average.
Step-by-step explanation:
The total number of measurements given is 2 + 12 + 10 + 33 + 40 + 76 + 80 + 65 + 52 + 22 + 12 + 5 + 11 = 420
If the mean is 21 mm and one standard deviation is 0.23 mm, then one standard deviation from the mean would be
21 ± 0.23
The lower limit is 20.77 mm
The upper limit is 21 + 0.23 = 21.23 mm
The number of measurements that fall within this range are
20.8 × 40
20.9 × 76
21.0 × 80
21.1 × 65
21.2 × 52
The total number of measurements that fall within this range is
40 + 76 + 80 + 65 + 52 = 313
The percentage of the measurements that fall within one standard deviation of the average is
313/420 × 100 = 74.5%
