The distance (in km) of 40 engineers from their residence . . .

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 probability that an engineer lives?

a) Less than 10 km from their place of work.

b) More than or equal to 10 km from their place of work.

c) Between 15 km to 30 km from their place of work.

Doubt by Aditi

Solution :

First of all, we should convert the above data into grouped frequency distribution table so that it because easy for us to solve it.

Distance (in km)	0-5	5-10	10-15	15-20	20-25	25-30	30-35	Total
No of Engineers	5	11	11	9	1	1	2	40

Total number of engineers = 40

P(E) = No. of favorable outcomes / Total No. of possible outcomes

a) No. of engineers who are living less than 10 Km from their place of work = 5+11 = 16

P(Engineer is living less than 10 km from their work)

= 16/40 = ⅖

b) No. of engineers who are living more than or equal to 10 Km from their place of work = 11+9+1+1+2=24

P(Engineer is living more than or equal to 10 km from their work)

= 24/40 = ⅗

Alternate Method
P(Engineer is living more than or equal to 10 km from their work) = 1 - P(Engineer is living less than 10 km from their work)

= 1 - ⅖
= ⅗ 

c) No. of engineers who are living between 15 km to 30 km from their place of work = 9 + 1 +1 = 11

P(Engineer is living between 15 km to 30 km)
= 11/40