(Answered) What is the probability

Statistics

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. Provide justifications and citations for your responses.

(a) If a random sample of 64 test scores is selected, what is the standard deviation of the sample mean?

(b) What is the probability that 64 randomly selected test scores will have a mean test score that is between 475 and 525?

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