Question

A distribution of sample means has a mean of 68, with a standard distribution of 12. Assuming a normal distribution, which sample mean would be most likely to be chosen at random from the population of sample means?

a) 49
b) 64
c) 74
d) 96

Answer 1

The most likely sample mean chosen at random from the population of sample means is 74.

Step-by-step explanation:

The distribution of sample means is approximately normal due to the Central Limit Theorem. According to the Central Limit Theorem, as the sample size increases, the distribution of sample means approaches a normal distribution regardless of the shape of the population distribution. Therefore, to determine which sample mean would be most likely chosen at random from the population of sample means, we need to find the sample mean that is closest to the population mean of 68.

Since 68 is the mean of the distribution of sample means, the sample mean that is closest to 68 would be the most likely to be chosen at random. From the given options, the sample mean closest to 68 is 74, so the answer is c) 74.