Question

Almost all medical schools in the United States require students to take the Medical College Admission Test (MCAT). To estimate the mean score of those who took the MCAT on your campus, you will obtain the scores of a simple random sample of students. The scores follow a normal distribution, and from published information, you know that the standard deviation of scores for all MCAT takers is 10.6. Suppose that (unknown to you) the mean score of those taking the MCAT on your campus is 510. You sample 25 students. What is the mean of the sampling distribution of their average score?

Answer 1

The mean of the sampling distribution of the average score for a sampled group taking the MCAT, with a true mean of 510 and given that the standard deviation is 10.6, is 510.

Step-by-step explanation:

The question asks to determine the mean of the sampling distribution of the average score for students who have taken the MCAT on a certain campus. The standard deviation of the MCAT scores is provided as 10.6, and it is given that these scores normally distribute. In addition, the size of the simple random sample is 25. Since the sampling distribution of the mean approaches a normal distribution due to the Central Limit Theorem, the mean of the sampling distribution of the average score (also known as the expected value) is equal to the true population mean, which in this case is stated to be 510 (although this information is supposedly unknown to the individual posing the question).

Therefore, the mean of the sampling distribution of the average MCAT score, for a sample size of 25, is 510.