SOLUTION: Assume the SAT Mathematics Level 2 test scores are normally distributed with a mean of 500 and a standard deviation of 100. Show all work. Just the answer, without supporting work

Question 1058760: Assume the SAT Mathematics Level 2 test scores are normally distributed with a mean of 500
and a standard deviation of 100. Show all work. Just the answer, without supporting work, will
receive no credit.
(a) Consider all random samples of 64 test scores. What is the standard deviation of the sample
means?
(b) What is the probability that 64 randomly selected test scores will have a mean test score that is
between 475 and 525?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Assume the SAT Mathematics Level 2 test scores are normally distributed with a mean of 500 and a standard deviation of 100. Show all work. Just the answer, without supporting work, will receive no credit.
(a) Consider all random samples of 64 test scores.
What is the standard deviation of the sample means?
Ans:: 100/sqrt(64) = 100/8 = 12.5
--------------------------------
(b) What is the probability that 64 randomly selected test scores will have a mean test score that is between 475 and 525?
z(475) = (475-500)/12.5 = -25/12.5 = -2
z(525) = (525-500)/12.5 = +25/12.5 = 2
---------
P(475<= x <=525) = P(-2<= z <=2) = normalcdf(-2,2) = 0.9545
-------------
Cheers,
Stan H.
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