Question

A population of values has a normal distribution with μ=20.7μ=20.7 and σ=16.8σ=16.8. You intend to draw a random sample of size n=169n=169.

Find P₅, which is the mean separating the bottom 5% means from the top 95% means.
P₅ (for sample means) =

Answer 1

Sol

xbar=sample mean=mu=20.7

sample sd=s=pop sd/sqr(n)=16.8/sqrt(169)=1.2923

z score for 5%=qnorm(0.05)=-1.644854

z=x-xbar/s

-1.644854=x-20.7/1.2923

x=-1.644854*1.2923+20.7

x=18.57436

P5 (for sample means) =18.6