Refer to Q.2, Exercise 14.2. What is the empirical probability that an engineer lives:
(i) less than $ 7 \mathrm{~km} $ from her place of work?
(ii) more than or equal to 7 km from her place of work?
(iii) within $\frac{1}{2}\ km$ from her place of work?
Given:
The distance (in km) of 40 engineers from their residence to their place of work were found as follows:
5 3 10 20 25 11 13 7 12 31 19 10 12 17 18 11 3 2 17 16 2 7 9 7 8 3 5 12 15 18 3 12 14 2 9 6 15 15 7 6 12
To do:
We have to find the empirical probability that an engineer lives:
(i) less than \( 7 \mathrm{~km} \) from her place of work.
(ii) more than or equal to 7 km from her place of work.
(iii) within $\frac{1}{2}\ km$ from her place of work.
Solution:
Total numbers of engineers $= 40$
(i) Number of engineers living less than $7\ km$ from her place of work $= 9$
Therefore,
The probability that an engineer lives less than 7 km from her place of work $= \frac{9}{40}$
(ii) Number of engineers living more than or equal to 7 km from her place of work $= 40-9$
$= 31$
Therefore,
The probability that an engineer lives more than or equal to 7 km from her place of work $= \frac{31}{40}$
(iii) Number of engineers living within $\frac{1}{2}\ km$ from her place of work $= 0$
Therefore,
The probability that an engineer lives within $\frac{1}{2}\ km$ from her place of work $= \frac{0}{40}$
$= 0$
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