Question

Scores on the Critical Reading part of the SAT exam in a recent year were roughly Normal with mean 495 and standard deviation 118. You choose an SRS of 100 students and average their SAT Critical Reading scores. The sampling distribution of the average score X-bar is

Answer 1

Answer: sample mean = 495

Explanation:

Given that :

Population mean = 495

Population standard deviation = 118

Sample size = 100

The sample mean according to the central limit theorem will be the same as the population mean ; According to the central limit theorem, the sample mean converges to the population mean as the sample size becomes larger, according to the theorem, usually once the SAMPLE size is greater than 30.

Here, the sample size is 100, Hence, the sample mean, will be equal to the population mean.

Sampling distribution of average score = 495 = population mean