Question #341265

A population of Grade 11 Arts and Design Students of size N=140 has mean grade of u=83 in Arts Subject and a population standard deviation of 25.




1.) What is the z-score of the the sample mean 80 if the sample size n=30?



2.) What is the area or probability of the sample mean 75 of the sample size n=30?



3.) What is the area greater than the sample mean of 80 if the sample size n=30?

1
Expert's answer
2022-05-16T16:20:40-0400

1)


z=xμσNnn(N1)=8083251403030(1401)=z=\dfrac{x-\mu}{\sigma\sqrt{\dfrac{N-n}{n(N-1)}}}=\dfrac{80-83}{25\sqrt{\dfrac{140-30}{30(140-1)}}}=

=0.738844=-0.738844

2)


P(X<75)=P(Z<7583251403030(1401))P(X<75)=P(Z<\dfrac{75-83}{25\sqrt{\dfrac{140-30}{30(140-1)}}})

P(Z<1.970251)=0.0244\approx P(Z<-1.970251)=0.0244

3)


P(X>80)=1P(Z8083251403030(1401))P(X>80)=1-P(Z\le\dfrac{80-83}{25\sqrt{\dfrac{140-30}{30(140-1)}}})

1P(Z<0.738844)=0.7700\approx 1-P(Z<-0.738844)=0.7700


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!
LATEST TUTORIALS
APPROVED BY CLIENTS