Final answer:
The mean of a uniformly distributed random variable can be calculated as the midpoint of the range of values.
Step-by-step explanation:
The question involves a random variable x that follows a uniform distribution. In a uniform distribution, all values within the given range are equally likely, and the distribution is represented by a rectangular shape on a graph. The mean is concise and can be stated without lengthy explanation.
It should also be noted that the student mentions a PDF (probability density function), which implies that the distribution of the random variable x is continuous. The Central Limit Theorem tells us that the sampling distribution of the sample mean will be normally distributed if the sample size is large enough, typically n > 30.
In the information given, it is stated that the random variable X has a known mean (25) and standard deviation (2). For a sample size of 100, the distribution of the sample mean can be expressed using the Central Limit Theorem.