Monthly salaries of 1000 workers
have a normal distribution with
mean of Rs 575 and standard deviation of Rs 75
Find number of workers having
salaries between Rs 500 and Rs 625?
Also find minimum salary of highest
paid 200 workers?
Answers
Given : Monthly salaries of 1000 workers have a normal distribution with
mean of Rs 575 and standard deviation of Rs 75
To find : number of workers having salaries between Rs 500 and Rs 625
minimum salary of highest paid 200 workers
Solution:
Mean Salary = Rs 575
SD = Rs 75
between Rs 500 and Rs 625
Z score = (Value - Mean)/SD
= ( 500 - 575 )/75
= - 1
=> 15.87 % workers having salary below this
(625 - 575)/75
= 50/75
= 2/3
= 0.667
=> 74.8 % workers having salary below this
salaries between Rs 500 and Rs 625 = 74.8 % - 15.87 % = 61 %
= 610
610 workers have salaries between Rs 500 and Rs 625
minimum salary of highest paid 200 workers
200 workers = 20 %
=> 80 % workers below salary of minimum salary of highest
paid 200 workers
=> z = 0.841
0.841 = ( Value - 575)/75
=> Value = 638
minimum salary of highest paid 200 workers = Rs 638
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