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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 32 17 16 2

7 9 7 8 3 5 12 15 18 3

12 14 2 9 6 15 15 7 6 12

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 1/2 km from her place of work?

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(i) Total number of engineers = 40

Number of engineers living less than 7 km from their place of work = 9

Hence, required probability that an engineer lives less than 7 km from her place of work, P = 9/40

(ii) Number of engineers living more than or equal to 7 km from their place of work = 40 − 9 = 31

Hence, required probability that an engineer lives more than or equal to 7 km from her place of work, P = 31/40

(iii) Number of engineers living within 1/2 km from her place of work = 0

Hence, required probability that an engineer lives within 1/2 km from her place of work, P = 0

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