Question

A population of 25 year- old female has a mean salary of P20,800 with a standard deviation of P1200. If a random sample of 10 is considered from the population, what is the probability that their salary is greater than P20900?

Answer 1

We have a normal distribution, 

$μ=20800,σ=1200,\\ n=10, \bar x=20900.$

Let's convert it to the standard normal distribution,

$\bar{z}=\cfrac{\bar{x}-\mu}{\sigma/\sqrt{n}},\\ \bar{z}=\cfrac{20900-20800}{1200/\sqrt{10}}=0.26,\\ P(\bar{X}>20900)=P(\bar{Z}>0.26)=\\ =1-P(\bar{Z}<0.26)=\\ =1-0. 6026=0.3974\text{ (from z-table).}$