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In Q-5, Exercise 14.2, you were asked to prepare a frequency distribution table, regarding the concentration of sulphur dioxide in the air in parts per million of a certain city for 30 days. Using this table, find the probability of the concentration of sulphur dioxide in the interval \( 0.12-0.16 \) on any of these days.
Given:
The data obtained for 30 days is as follows:
0.03 0.08 0.08 0.09 0.04 0.17 0.16 0.05 0.02 0.06 0.18 0.20 0.11 0.08 0.12 0.13 0.22 0.07 0.08 0.01 0.10 0.06 0.09 0.18 0.11 0.07 0.05 0.07 0.01 0.04
To do:
We have to find the probability of the concentration of sulphur dioxide in the interval \( 0.12-0.16 \) on any of these days.
Solution:
The frequency distribution table of the given data is as follows:
Interval | Frequency |
0.01-0.04 | 5 |
0.04-0.08 | 11 |
0.08-0.12 | 7 |
0.12-0.16 | 2 |
0.16-0.20 | 4 |
0.20-0.24 | 1 |
Total | 30 |
Total number of days in which the data was recorded $= 30$ days
Numbers of days in which sulphur dioxide was present in between the interval $0.12-0.16 = 2$ days
Therefore,
The probability of the concentration of sulphur dioxide in the interval $0.12-0.16$ on any of these days $= \frac{2}{30}$
$= \frac{1}{15}$