A population with mean $m$ and standard deviation 5 follows a normal distribution. A sample of size 36 is randomly extracted, and the 99\% confidence interval for the population mean $m$ obtained using the sample mean is $1.2 \leq m \leq a$. What is the value of $a$? (When $Z$ is a random variable following the standard normal distribution, calculate using $\mathrm { P } ( | Z | \leq 2.58 ) = 0.99$.) [3 points]
(1) 5.1
(2) 5.2
(3) 5.3
(4) 5.4
(5) 5.5

9. A company commissioned a polling organization to survey the percentage of residents in locations A and B who have heard of a certain product (hereinafter referred to as ``awareness''). The results are as follows: At a 95\% confidence level, the confidence intervals for the product's awareness in locations A and B are $[0.50, 0.58]$ and $[0.08, 0.16]$ respectively. Which of the following options are correct?
(1) In location A, 54\% of the survey respondents have heard of the product
(2) The number of survey respondents in location B was less than in location A
(3) The survey results can be interpreted as: the probability that more than half of all residents in location A have heard of the product is greater than 95\%
(4) If multiple surveys are conducted in location B using the same method, the awareness has a 95\% chance of falling in the interval $[0.08, 0.16]$
(5) After intensive advertising, a follow-up survey is conducted in location B with the number of respondents increased to four times the original number. Then at a 95\% confidence level, the width of the confidence interval for the product's awareness will be reduced by half (i.e., 0.04)

12. A sampling survey was conducted to understand the level of support among Taiwan's citizens for a certain issue. The results, classified by gender, are shown in the table below:

	Female Citizens	Male Citizens
Proportion supporting the issue $\hat{p}$	0.52	0.59
Standard deviation of $\hat{p}$: $\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$	0.02	0.04

Which of the following conclusions can be drawn from this sampling result?
(1) The proportion of male citizens in Taiwan supporting this issue is greater than the proportion of female citizens supporting this issue
(2) At a 95\% confidence level, the confidence interval for the proportion of female citizens in Taiwan supporting this issue is $[0.48, 0.56]$ (rounded to the second decimal place)
(3) The number of female citizens in this sample is less than the number of male citizens
(4) If gender is not distinguished, the proportion of people in this sample supporting the issue $\hat{p}$ is between 0.52 and 0.59
(5) If gender is not distinguished, the standard deviation of $\hat{p}$ in this sample $\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$ is between 0.02 and 0.04

Part II: Fill-in-the-Blank Questions (40 points)

Instructions