Answer:
15.85%
Step-by-step explanation:
The empirical rule states that:
- 68% of all data falls within 1 standard deviation of the mean
- 95% of all data falls within 2 standard deviation of the mean
- 99.7% of all data falls within 3 standard deviation of the mean
When we say 1,2,3 standard deviation of the mean, that is, it is evenly distributed in both sides of the mean. For example:
68/2 = 34% of data falls within mean - 1*standard deviation, and
also, 34% of data falls within mean + 1*standard deviation
Now, we see that 192 - 27 = 165, so this is 1 standard deviation of the mean [mean - 1*standard deviation], so 34% of data fall in that range.
But we want, data that ARE FEWER than 165. So, we use property of normal distribution.
Half of data (50%) is left of mean, of which 34% fall within 1 standard deviation So the remaining would fall fewer than 165.
That is 50 - 34 = 16 - 0.15 = 15.85%
<u><em>Note:</em></u> since 99.7% fall within 3 standard deviation of mean, so 100 - 99.7 = 0.3 which is distributed in both sides, so 0.3/2=0.15 is subtracted
