Answer:
For (a), the mean of the sampling distribution for x¯ is 25.5.
For (b), the standard deviation of the sampling distribution for x¯ is approximately 1.386.
Explanation:
According to the Central Limit Theorem, for samples of size 12 from a normally distributed random variable x with a mean of μ=25.5 and a standard deviation of σ=4.8:
(a) The mean of the sampling distribution for x¯ is also μ=25.5. This means that, on average, the sample mean will be equal to the population mean. In this case, the sample mean is denoted as x¯.
(b) The standard deviation of the sampling distribution for x¯ is σ/√n, where n is the sample size. So, for a sample size of 12, the standard deviation of the sampling distribution for x¯ would be σ/√12.
Substituting the given values, the standard deviation of the sampling distribution for x¯ would be 4.8/√12, which is approximately 1.386.
To summarize:
(a) The mean of the sampling distribution for x¯ is 25.5.
(b) The standard deviation of the sampling distribution for x¯ is approximately 1.386.