Final answer:
The Central Limit Theorem states that the sample mean of a large enough sample size tends to follow a normal distribution regardless of the shape of the population distribution. In this case, we have a random sample of scores on an exam with a mean of 81 and standard deviation of 15/√2000.
Step-by-step explanation:
The given question is related to the Central Limit Theorem. The Central Limit Theorem states that the sample mean of a large enough sample size tends to follow a normal distribution regardless of the shape of the population distribution. In this case, we have a random sample of scores on an exam, which is assumed to have an approximate normal distribution. With a sample size of 2000, we can apply the Central Limit Theorem to analyze the distribution of the sample means.
The mean of the distribution of the sample means is equal to the mean of the population, which is 81 points in this case. The standard deviation of the distribution of the sample means is equal to the standard deviation of the population divided by the square root of the sample size, which is 15/√2000.
Therefore, the distribution of the sample mean is approximately normal with a mean of 81 and a standard deviation of 15/√2000.