  Question

The distance (in km) of $$40$$ engineers from their residence to their place of work were found as follows:$$\begin{matrix} 5 & 3 & 10 & 20 & 25 & 11 & 13 & 7 & 12 & 31 \\ 19 & 10 & 12 & 17 & 18 & 11 & 32 & 17 & 16 & 2 \\ 7 & 9 & 7 & 8 & 3 & 5 & 12 & 15 & 18 & 3 \\ 12 & 14 & 2 & 9 & 6 & 15 & 15 & 7 & 6 & 12 \end{matrix}$$What is the empirical probability that an engineer lives:(i) less than $$7\ km$$ from her place of work?(ii) more than or equal to $$7\ km$$ from her place of work?(iii) within $$\dfrac{1}{2}\ km$$ from her place of work?

Solution

Distance (in km.) No. of engineers Less than $$7\ km.$$ $$9$$ More than $$7\ km.$$ $$31$$ Total$$40$$ Total number of engineers $$= 40$$(i) Number of engineers living less than $$7 km$$ from their place of work $$=9$$$$P= \dfrac{9}{40}$$(ii) Number of engineers living more than or equal to $$7 km$$ from their place of work $$= 40-9 = 31$$$$P= \dfrac{31}{40}$$(iii) Number of engineers living within $$\dfrac{1}{2}km$$ from her place of work $$= 0$$$$P= \dfrac{0}{40} = 0$$MathematicsNCERTStandard IX

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