Hi! please help me solve my this

Question

The monthly income of the workers at the Microsoft plant are distributed normally. Suppose the mean monthly income is P30,000 and the standard deviation is P5,000. 20% of workers earn how much per month?

Answer 1

In this problem you need a to find the zscore

We know that we are looking at 20 % of the sample which write as 0.2

Since the least value in the positive z score table is 0.5 we do a subtraction:

1- (positive z score) = (negative z score) which the 20% of the workers have

the positive zscore (in the table corressponding to 0.7995) is 0.84

since 1-(0.2)= 0.8 and 0.7995 is nearest 0.8 on z score table

using the equation for zscore you get:

0.84 = (x -(30000))/(5000)

multiplying 0.84 by 5000 and adding 30000 (solving for x)

you get the answer x = $34,200 (per 20% of the workers make on average) !!