Question

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 $\frac{1}{2}$ km from her place of work?

Answer 1

The distance (in km) of 40 engineers from their residence to their place of work was 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 $=\frac{9}{40}$

(ii) Number of engineers living more than or equal to 7 km from their place of work

= 40 – 9 = 31

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 km from their place of work = 0

The probability that an engineer lives within km from her place of work $=\frac{0}{40}=0$