Answer to Question #88827 in Statistics and Probability for Amelia

Question #88827
Each of the following samples was obtained from a population with µ = 100 and σ = 10. Find
the z-score corresponding to each sample mean.
a. M = 95 for a sample of n = 4
b. M = 104 for a sample of n = 25
c. M = 103 for a sample of n = 100
1
Expert's answer
2019-05-01T11:09:57-0400

If X has a distribution with mean μ,\mu, and standard deviation σ,\sigma, and is approximately normally distributed or nn is large, then the sample mean M is approximately normally distributed with mean μ\mu and standard error σ/n.\sigma/\sqrt{n}.


z=Mμσ/nz={M-\mu \over \sigma/\sqrt{n}}

Given that μ=100\mu=100 and σ=10.\sigma=10.

a. M = 95 for a sample of n = 4 


z=9510010/4=1z={95-100 \over 10/\sqrt{4}}=-1

b. M = 104 for a sample of n = 25 


z=10410010/25=2z={104-100 \over 10/\sqrt{25}}=2

c. M = 103 for a sample of n = 100


z=10310010/100=3z={103-100 \over 10/\sqrt{100}}=3


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!

Leave a comment