Questions: Using the sampling distribution shown in Figure 1, indicate whether each sample mean is (i) reasonably likely to occur, (ii) unusual but might occur occasionally, or (iii) extremely unlikely to ever occur.
(a) x̄=250 is
(b) x̄=303 is
(c) x̄=312 is
Transcript text: Using the sampling distribution shown in Figure 1, indicate whether each sample mean is.(i) reasonably likely to occur, (ii) unusual but might occur occasionally, or (iii) extremely unlikely to ever occur.
(a) $\bar{x}=250$ is $\square$
(b) $\bar{x}=303$ is $\square$
(c) $\bar{x}=312$ is $\square$
Solution
Solution Steps
Step 1: Analyze the sampling distribution
The sampling distribution is centered around 300 and appears approximately normal. Most of the distribution lies between 290 and 310.
Step 2: Evaluate (a) x̄ = 250
A sample mean of 250 is far outside the main range of the distribution, making it extremely unlikely.
Step 3: Evaluate (b) x̄ = 303
A sample mean of 303 falls within the common range of the distribution and close to the center, making it reasonably likely.
Step 4: Evaluate (c) x̄ = 312
A sample mean of 312 is outside the typical range but still close enough that it might occur occasionally.
Final Answer:
(a) extremely unlikely to ever occur
(b) reasonably likely to occur
(c) unusual but might occur occasionally