Question

The distance (in km) of 40 engineers from their residence to their place of work were found as follows.
$\begin{array}{cccccccccc}5& 3& 10& 20& 25& 11& 13& 7& 12& 31\\ 19& 10& 12& 17& 18& 11& 32& 17& 16& 2\\ 7& 9& 7& 8& 3& 5& 12& 15& 18& 3\\ 12& 14& 2& 9& 6& 15& 15& 7& 6& 12\end{array}$
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

Total number of engineers = 40
(i) Number of engineers living less than 7 km from their place of work= 9
Hence, the required probability that an engineer lives less than 7 km from her place of Work is,
$P=\frac{9}{40}$.
(ii) Number of engineers living more than or equal to 7km from their place of work = 40 −9= 31
Hence, required probability that an engineer lives more than or equal to 7km from her place of work, $P=\frac{31}{40}$
(iii) Number of engineers living within $\frac{1}{2}$ km from their place of work= 0
Hence, required probability that an engineer lives within $\frac{1}{2}$ km from her place of work, P =0