Refer to Q.2, Exercise 14.2. 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 ½ km from her place of work?

 Solution:

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

Total numbers of engineers = 40

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

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

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

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

(iii) Number of engineers living within ½ km from their place of work = 0

∴, the probability that an engineer lives within ½ km from her place of work = 0/40 = 0