Find P29, which is the mean separating the bottom 29% means from the top 71% means.

Question

A population of values has a normal distribution with  and . You intend to draw a random sample of size . Find P29, which is the mean separating the bottom 29% means from the top 71% 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

z = (sample mean - population mean)/(standard deviation/square root(sample size)

from standard normal probability tabular lookup the z value for 29th percentile is approximately -0.55 so

-0.55 = (sample mean - 224.9)/(13.2/sqrt(220)

-0.55 * (13.2/sqrt(220) + 224.9 = sample mean

224.411 = sample mean