Question

The student test scores for a nationwide standardized test have an unknown distribution with mean 259 and standard deviation 38 points. A sample, with size n=55, was randomly drawn from the population. Using the Central Limit Theorem for Means, what is the mean for the sample mean distribution?

Answer 1

The mean for the sample mean distribution, given a sample size of 55 and using the Central Limit Theorem for Means, is 259 as it will equal the population mean.

Step-by-step explanation:

The student has asked about the mean for the sample mean distribution when a sample size of n=55 is drawn from a population with a mean of 259 and a standard deviation of 38 points, using the Central Limit Theorem for Means.

According to the Central Limit Theorem for Means, the distribution of the sample mean will be approximately normal if the sample size is large enough.

Moreover, the theorem states that the mean of the sample mean distribution will equal the population mean. Thus, for a nationwide standardized test with a population mean of 259, regardless of the unknown distribution of the student test scores, the mean for the sample mean distribution is also 259.