SOLUTION: Please help with this: Assume the SAT test scores are normally distributed with a mean of 500 and a standard deviation of 100. Please show all work. (a) Consider all random

Algebra ->  Probability-and-statistics -> SOLUTION: Please help with this: Assume the SAT test scores are normally distributed with a mean of 500 and a standard deviation of 100. Please show all work. (a) Consider all random       Log On


   



Question 1052856: Please help with this:
Assume the SAT test scores are normally distributed with a mean of 500 and a standard deviation of 100. Please show all work.
(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?
Thank you for your help!

Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
The standard deviation of the sample means is the original sd/sqrt(n) the sample size
That would be 100/sqrt(64)=100/8=12.5
The probability 64 randomly selected test scores will be between 475 and 525 is the probability z is between -2 and 2, or 0.9545. \
z=(x-mean)/sd