Question

(1 point) A variable of a population has a mean of I = 250 and a standard deviation of o = 49.

Answer 1

Question 1a:

- The population mean and sample mean are approximately the same in theory. The only difference is that the distribution of the sample will be wider due to a larger uncertainty caused by having less data to work with.

- Thus, we have:

`\begin{gathered} \text{ Sample Mean:} \\ 250 \\ \\ \text{ Standard Deviation:} \\ (\sigma)/(√(n))=(49)/(√(49))=(49)/(7)=7 \\ \end{gathered}`

Question 1b:

- The assumption is that the distribution is a normal distribution (OPTION C)

Question 1c:

Yes, the sampling distribution of the sample mean is always normal (OPTION B). This is in accordance with the central limit theorem.