Question

Scores on the mathematics part of the SAT exam in a recent year were roughly Nonnal with mean 523 and standard devation 120. You choose an SRS of 100 students and average their SAT math scores. If you do this many times, with a sample of size 100 each lime, the mean of the average scores will get close to

A. 523
B. 523
C. 5.23
D. None of the above

Answer 1

The mean of the average SAT math scores from multiple SRS of 100 students each will get close to the population mean of 523.

Step-by-step explanation:

The correct option : A. 523.

According to the Central Limit Theorem, when you take an SRS (Simple Random Sample) of a certain size from a population with a mean μ and standard deviation σ, the distribution of the sample means will be approximately normal, assuming the sample size is large enough (usually n ≥ 30 is considered sufficient). This is known as the sampling distribution of the mean. For the SAT math scores, which we are told are normally distributed, the sample means will also be normally distributed, with a mean equal to the population mean (μ). Thus, when you repeatedly take samples of 100 students and calculate the mean SAT math score for each sample, the mean of those average scores will get close to the population mean, which is 523.

The standard deviation of the sampling distribution, known as the standard error, would be σ/√n where σ is the population standard deviation and n is the sample size. However, for this question, we are only looking to identify the expected mean of the sample means, which remains 523, regardless of the standard deviation of the individual scores.