Question

A sample of n = 14 observations is drawn from a normal population with μ=1040 and σ=230. Find each of the following:

A. P(x̄>1162)

B. P(x̄<910)

C. P(x̄>990)

Answer 1

Solution:

n=14

$\bar X\sim N(\mu_x,\sigma_x) \\\mu_x=\mu=1040 \\\sigma_x=\dfrac{\sigma}{\sqrt n}=\dfrac{230}{\sqrt{14}}=61.47$

A. P(x̄>1162)$=P(z>\dfrac{1162-1040}{61.47})=P(z>1.98)=1-P(z\le 1.98)=1-0.97615=0.02385$

B. P(x̄<910)$=P(z<\dfrac{910-1040}{61.47})=P(z<-2.11)=1-P(z<2.11)=1-0.98257=0.01743$

C. P(x̄>990)$=P(z>\dfrac{990-1040}{61.47})=P(z>-0.81)=1-P(z\le -0.81)=P(z\le 0.81)=0.79103$