Suppose the weight of products produced at a certain factory follows a normal distribution $\mathrm { N } \left( 11,2 ^ { 2 } \right)$. Two people, $A$ and $B$, each independently extracted a sample of size 4. Using the standard normal distribution table on the right, what is the probability that the sample means extracted by both $A$ and $B$ are between 10 and 14 inclusive? [3 points]

$z$	$\mathrm { P } ( 0 \leqq Z \leqq z )$
1	0.3413
2	0.4772
3	0.4987

(1) 0.8123
(2) 0.7056
(3) 0.6587
(4) 0.5228
(5) 0.2944

The weight of products manufactured at a certain factory follows a normal distribution $\mathrm { N } \left( 11,2 ^ { 2 } \right)$. Two people A and B each independently randomly extracted a sample of size 4. Using the standard normal distribution table on the right, what is the probability that the sample means of both A and B are between 10 and 14 inclusive? [3 points]

$z$	$\mathrm { P } ( 0 \leqq Z \leqq z )$
1	0.3413
2	0.4772
3	0.4987

(1) 0.8123
(2) 0.7056
(3) 0.6587
(4) 0.5228
(5) 0.2944

At a certain factory, table tennis balls are dropped onto a steel floor from a fixed height, and the height to which the table tennis ball bounces follows a normal distribution. When 100 table tennis balls produced by this factory were randomly sampled and the bounce height was measured, the mean was 245 and the standard deviation was 20. What is the number of integers in the 95\% confidence interval for the mean bounce height of all table tennis balls produced by this factory? (Note: The unit of height is mm, and when $Z$ follows a standard normal distribution, $\mathrm { P } ( 0 \leqq Z \leqq 1.96 ) = 0.4750$.) [3 points]
(1) 5
(2) 6
(3) 7
(4) 8
(5) 9

Let $\bar { X }$ be the sample mean of a sample of size 25 randomly extracted from a population that follows a normal distribution with population mean 75 and population standard deviation 5. For a random variable $Z$ following the standard normal distribution, a positive constant $c$ satisfies
$$\mathrm { P } ( | Z | > c ) = 0.06$$
Which of the following in are correct? [4 points]
ㄱ. For a constant $a$ such that $\mathrm { P } ( Z > a ) = 0.05$, we have $c > a$. ㄴ. $\mathrm { P } ( \bar { X } \leqq c + 75 ) = 0.97$ ㄷ. For a constant $b$ such that $\mathrm { P } ( \bar { X } > b ) = 0.01$, we have $c < b - 75$.
(1) ㄱ
(2) ㄷ
(3) ㄱ, ㄴ
(4) ㄴ, ㄷ
(5) ㄱ, ㄴ, ㄷ

A company manufactures women's general handball balls certified by the International Handball Federation. The weight of handball balls produced by this company follows a normal distribution with mean 350 g and standard deviation 16 g. The company determines that there is a problem in the production process if the average weight of 64 randomly selected handball balls is 346 g or less, or 355 g or more. Using the standard normal distribution table below, what is the probability that the company determines there is a problem in the production process? [3 points]

$z$	$\mathrm { P } ( 0 \leqq Z \leqq z )$
2.00	0.4772
2.25	0.4878
2.50	0.4938
2.75	0.4970

(1) 0.0290
(2) 0.0258
(3) 0.0184
(4) 0.0152
(5) 0.0092

The duration of one use of a public bicycle in a certain city follows a normal distribution with mean 60 minutes and standard deviation 10 minutes. When 25 uses of the public bicycle are randomly sampled and surveyed, what is the probability that the total duration of the 25 uses is 1450 minutes or more, using the standard normal distribution table on the right? [3 points]

$z$	$\mathrm { P } ( 0 \leqq Z \leqq z )$
1.0	0.3413
1.5	0.4332
2.0	0.4772
2.5	0.4938

(1) 0.8351
(2) 0.8413
(3) 0.9332
(4) 0.9772
(5) 0.9938

The length $X$ of products manufactured at a certain factory follows a normal distribution with mean $m$ and standard deviation 4. When $\mathrm { P } ( m \leq X \leq a ) = 0.3413$, what is the probability that the sample mean of the lengths of 16 products randomly selected from this factory is at least $a - 2$, using the standard normal distribution table on the right? (where $a$ is a constant and the unit of length is cm) [4 points]

$z$	$\mathrm { P } ( 0 \leq Z \leq z )$
1.0	0.3413
1.5	0.4332
2.0	0.4772

(1) 0.0228
(2) 0.0668
(3) 0.0919
(4) 0.1359
(5) 0.1587

From a population following a normal distribution $\mathrm { N } \left( 50,8 ^ { 2 } \right)$, a sample of size 16 is randomly extracted to obtain the sample mean $\bar { X }$. From a population following a normal distribution $\mathrm { N } \left( 75 , \sigma ^ { 2 } \right)$, a sample of size 25 is randomly extracted to obtain the sample mean $\bar { Y }$. When $\mathrm { P } ( \bar { X } \leq 53 ) + \mathrm { P } ( \bar { Y } \leq 69 ) = 1$, what is the value of $\mathrm { P } ( \bar { Y } \geq 71 )$ using the standard normal distribution table below?

$z$	$\mathrm { P } ( 0 \leq Z \leq z )$
1.0	0.3413
1.2	0.3849
1.4	0.4192
1.6	0.4452

[4 points]
(1) 0.8413
(2) 0.8644
(3) 0.8849
(4) 0.9192
(5) 0.9452

The content volume of a cosmetic product produced by a factory follows a normal distribution with mean 201.5 g and standard deviation 1.8 g. Find the probability that the sample mean of 9 randomly selected cosmetic products from this factory is at least 200 g using the standard normal distribution table on the right. [4 points]

$z$	$\mathrm { P } ( 0 \leq Z \leq z )$
1.0	0.3413
1.5	0.4332
2.0	0.4772
2.5	0.4938

(1) 0.7745
(2) 0.8413
(3) 0.9332
(4) 0.9772
(5) 0.9938

A cosmetic product produced at a certain factory has a content weight that follows a normal distribution with mean 201.5 g and standard deviation 1.8 g. Using the standard normal distribution table on the right, what is the probability that the sample mean of 9 randomly selected cosmetic products from this factory is at least 200 g? [3 points]

$z$	$\mathrm { P } ( 0 \leq Z \leq z )$
1.0	0.3413
1.5	0.4332
2.0	0.4772
2.5	0.4938

(1) 0.7745
(2) 0.8413
(3) 0.9332
(4) 0.9772
(5) 0.9938