Final answer:
The assumption about the sample size (n) is necessary to assume the distribution of sample means of a population with a uniform distribution is normally distributed.
Step-by-step explanation:
The assumption about the sample size (n) is necessary before we can assume the distribution of sample means of a population with a uniform distribution is normally distributed.
The Central Limit Theorem states that if the size of the sample is sufficiently large, the distribution of the sample means will be approximately normal regardless of the shape of the population.
The mean of the sample means will equal the population mean, and the standard deviation of the distribution of the sample means, called the standard error of the mean, is equal to the population standard deviation divided by the square root of the sample size (n).
To determine if the sample size is large enough, it is generally recommended to have at least 30 samples or ensure that the data comes from a normal distribution.