Question

A population of values has a normal distribution with μ=9.1μ=9.1 and σ=14.1σ=14.1. You intend to draw a random sample of size n=167n=167.

Find P₃₀, which is the mean separating the bottom 30% means from the top 70% means.
P₃₀ (for sample means) =

Enter your answers as numbers accurate to 1 decimal place. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

Answer 1

We have to find P30 the sample mean separating bottom 30% means from top 70% means

P30 = + ( /√n) * Z​​​​​​0.30

Where Zo.30 is Z score that corresponding to bottom 0.30 area

Using Z table Z​​​​​​0.30 = -0.52

P30 = 9.1 + (14.1/√167)*(-0.524)

P30 = 8.5