Question

Scores on the mathematics part of the SAT exam in a recent year were roughly Normal with mean 507 and standarddeviation 108. You choose an SRS of 100 students and average their SAT math scores. If you do this many times, with asample of size 100 each time, the mean of the average scores will get close to

Answer 1

SOLUTION

The central limit theorem (CLT) states that the distribution of sample means approximates a normal distribution as the sample size gets larger, regardless of the population's distribution. Sample sizes equal to or greater than 30 are often considered sufficient for the CLT to hold.

From this theorem, since the sample size (100) is greater than 30, the theorem holds true. So the mean of the average score will still be or get close to 507.

Hence the aswer is option B