Answer to Question #351017 in Statistics and Probability for Malavika

Question

. In a manufacturing organisation, the distribution of wages was perfectly

normal and the number of workers employed in the organisation was 5000.

The mean wages of the workers were calculated at Rs. 800 and standard

deviation was worked out to be Rs. 200. On the basis of the information

estimate:

(i) The number of workers getting salary between Rs.700 and Rs.900.

(ii) Percentage of workers getting salary above Rs.1000

(iii) Percentage of workers getting salary below Rs.600

Answer 1

(i)

$$P(700<X<900)=P(Z<\dfrac{900-800}{200})$$

$$-P(Z\le\dfrac{700-800}{200})$$

$$=P(Z<0.5)-P(Z\le-0.5)$$

$$\approx0.69146-0.30854\approx0.3829$$

$0.3829(500)=1915$ workers

(ii)

$$P(X>1000)=1-P(Z\le\dfrac{1000-800}{200})$$

$$=1-P(Z\le1)\approx0.1587$$

$15.87$ %

(iii)

$$P(X<600)=P(Z<\dfrac{600-800}{200})$$

$$=P(Z<-1)\approx0.1587$$

$15.87$ %