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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 $= \frac{2}{30}$

$= \frac{1}{15}$

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