Question

A sample of n=21 observations is drawn from a normal population with m=1030 and standard deviation=200. Find each of the following:

A. P(X >1108)

B. P(X < 942)

C. P(X > 999)

Answer 1

A. $P(\bar X>1108)=P(Z>\frac{1108-1030}{\frac{200}{\sqrt{21}}})=P(Z>1.79)=0.0367.$

B. $P(\bar X<942)=P(Z<\frac{942-1030}{\frac{200}{\sqrt{21}}})=P(Z<-2.02)=0.0217.$

C. $P(\bar X>999)=P(Z>\frac{999-1030}{\frac{200}{\sqrt{21}}})=P(Z>-0.71)=0.7611.$