SOLUTION: Please Help Consider a normal population with µ = 25 and σ = 7.0. (A) Calculate the standard score for a value x of 24. (B) Calculate the standard score for a randoml

Algebra ->  Probability-and-statistics -> SOLUTION: Please Help Consider a normal population with µ = 25 and σ = 7.0. (A) Calculate the standard score for a value x of 24. (B) Calculate the standard score for a randoml      Log On


   

Question 638353: Please Help
Consider a normal population with µ = 25 and σ = 7.0.
(A) Calculate the standard score for a value x of 24.
(B) Calculate the standard score for a randomly selected sample of 30 with x = 24.
(C) Explain why the standard scores of 24 are different between A and B above.
This is what I have but am not sure if it correct.
(A) z(24)= (24-25)/7
(-1)/7=-0.1429
(B) z(24) = (24-25)/(7/sqrt30)
(-1)/(7/900)
(-1)/(128)=-0.0078
(C) The sample mean is the same as the population mean and the sample mean standard deviation is sqrt(n).
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
A)
Correct

B)
This should be closer to -0.782460796.

Note: sqrt(30) is NOT 900

C)
The difference between the two is that the standard deviations aren't the same. In the first, the standard deviation is simply sigma. In the second, the standard deviation is sigma/sqrt(n) -- this is known as the standard error of the mean. This affects the shape/spread of the distribution, which in turn affects how far the data value is from the mean. This then changes/affects the z-score.