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 $7km$ from her place of work?
(ii) more than or equal to $7km$ from her place of work?
(iii) within $\frac{1}{2}km$ from her place of work?

Answer 1

Distance (in km.)	No. of engineers
Less than $7km.$	$9$
More than $7km.$	$31$
Total	$40$

Total number of engineers $=40$

(i) Number of engineers living less than $7km$ from their place of work $=9$
$P=\frac{9}{40}$

(ii) Number of engineers living more than or equal to $7km$ from their place of work $=40-9=31$
$P=\frac{31}{40}$

(iii) Number of engineers living within $\frac{1}{2}km$ from her place of work $=0$
$P=\frac{0}{40}=0$