We have the interval 12.8 < μ < 34.9.
If this is the 95% confidence interval, there is a 95% chance that the population mean falls within this interval.
The population mean has only one value, but we can not know it from taking samples. We can only estimate it.
That's what is done when finding the confidence interval for the population mean: we estimate a interval for the population mean with a certain chance (it never reaches 100%) from the information of the sample mean, standard deviation (from the sample or the population) and sample size.
The first statement is not correct:
Our sample mean is (12.8+34.9)/2=23.85. We know it because the sample mean is always at the center of the confidence interval. The population mean has a certin value, but we do not know with certainty.
The second statement is not correct:
We can not expect the sample means to be in the interval with a chance of 95%.
The third statement is not correct:
The confidence interval does not give information about the probability of individual widths.
The fourth and fifth statements are correct.
Answer: Fourth and fifth statements are correct.