Question

A population of values has a normal distribution with μ = 86.7 and σ = 75 . You intend to draw a random sample of size n = 35 .

Find P7, which is the score separating the bottom 7% scores from the top 93% scores. P7 (for single values) =

Find P7, which is the mean separating the bottom 7% means from the top 93% means. P7 (for sample means) =

Answer 1

Find P7, which is the score separating the bottom 7% scores from the top 93% scores.

use pnormgC in R to get the bottom 7%

library(tigerstats)
qnormGC(0.07,region="below",mean=86.7,sd=75,graph=TRUE)

P7=-23.98

Find P7, which is the mean separating the bottom 7% means from the top 93% means. P7 (for sample means)

sample mean =xbar=86.7

sample standard deviation=sigma/sqrt(n)=75/sqrt(35)=12.67731

Rcode

library(tigerstats)
qnormGC(0.07,region="below",mean=86.7,sd=12.67731,graph=TRUE)

ANSWER;

P(7)=67.99