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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 $$= 0$$
$$P= \dfrac{0}{40} = 0$$

Mathematics
NCERT
Standard IX

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