<em>So</em><em> </em><em>the</em><em> </em><em>right</em><em> </em><em>ans</em><em> </em><em>is</em><em> </em><em>3</em><em>%</em><em>.</em>
<em>Look</em><em> </em><em>at</em><em> </em><em>the</em><em> </em><em>attached</em><em> </em><em>picture</em><em>⤴</em>
<em>Hope</em><em> </em><em>it</em><em> </em><em>will</em><em> </em><em>help</em><em> </em><em>u</em><em>.</em><em>.</em><em>.</em>
No, this is not a plausible value for the population mean, because 5 is not within the 95% confidence interval.
====================================================
Explanation:
The greek letter mu is the population mean. It has the symbol which looks like the letter 'u' but with a tail at the front or left side.
The question is asking if mu = 5 is plausible if the researcher found the 95% confidence interval to be 5.2 < mu < 7.8
We see that 5 is <u>not</u> in that interval. It's a bit to the left of 5.2
Since mu = 5 is not in the interval, it's not a plausible value for the population mean.
Have we ruled it out with 100% confidence? No. Such a thing is not possible. There's always room for (slight) error. The researcher would need to do a census to be fully confident; however, such practices are very time consuming and expensive. This is the main reason why statistics is important to try to estimate the population with a sample.