Question

In a sample of 120 workers in a factory, the mean and s.d. of wages were
Rs 11.35 and Rs 3.03 respectively. Find the percentage of workers getting
wages between Rs 9 and Rs 17 in the whole factor, assuming that the vages
are normally distributed. (Given, Area under standard normal curve from z =
R20 to z = 0.78 is 0.2823 and to z= 1.86 is 0.4686). ​

Answer 1

Answer:

75%

Step-by-step explanation:

Given,

n = 120  ( total workers)

μ = 11.35  ( mean)

σ = 3.03  (S.D.)

To find the percentage of workers getting wages between Rs.9 and Rs.17 in the whole factory assuming that the wages are normally distributed is :

= P( 9 ≤ X ≤ 17)

= P( [ 9 - μ ] / σ ≤ [X - μ] / σ ≤ [ 17 - μ ] / σ )

= P( [ 9-11.35 ] / 3.03 ≤ z ≤ [ 17-11.35 ] / 3.03 ) ; z = [X - μ ] / σ is the standard normal variable

= P(-0.776 ≤ z ≤ 1.865 )

= P(z ≤ 1.865 ) - P( z ≤ -0.776 )

= 0.96891 - 0.21887

= 0.75

= 0.75 * 100

= 75%