# Refer to Q.2, Exercise 14.2. What is the empirical probability that an engineer lives:(i) less than $7 \mathrm{~km}$ 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?

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Given:

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

To do:

We have to find the empirical probability that an engineer lives:

(i) less than $7 \mathrm{~km}$ 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.

Solution:

Total numbers of engineers $= 40$

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

Therefore,

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 her place of work $= 40-9$

$= 31$

Therefore,

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 $\frac{1}{2}\ km$ from her place of work $= 0$

Therefore,

The probability that an engineer lives within $\frac{1}{2}\ km$ from her place of work $= \frac{0}{40}$

$= 0$

Updated on 10-Oct-2022 13:47:38