Question

How many workers have salary above $2675 in the distribution whose average salary is $2400 and standard deviation is $100 and the number of workers in the factory is 15000. If the salary of workers follows the normal law?

Answer 1

Solution:

Given, $\mu=\$2400,\sigma=\$100,n=15000$

$X\sim N(\mu,\sigma)$

$P(X>2675)=P(z>\dfrac{2675-2400}{100})=P(z>2.75)=1-P(z\le2.75) \\=1-0.99702=0.00298$

Now, the number of workers having salary greater than $2675$=0.00298\times15000=44.7\approx44$