The following table shows the results of a survey on customer preferences for hiking boots by manufacturer at a certain department store.

Manufacturer	A	B	C	D	Total
Preference (\%)	20	28	25	27	100

When 192 customers each purchase one pair of hiking boots, what is the probability that 42 or more customers will choose product C, using the standard normal distribution table on the right? [3 points]

$z$	$\mathrm { P } ( 0 \leqq Z \leqq z )$
0.5	0.1915
1.0	0.3413
1.5	0.4332
2.0	0.4772

(1) 0.6915
(2) 0.7745
(3) 0.8256
(4) 0.8332
(5) 0.8413

The following is a table showing customer preference by manufacturer for hiking boots sold at a certain department store.

Manufacturer	A	B	C	D	Total
Preference (\%)	20	28	25	27	100

When 192 customers each purchase one pair of hiking boots, what is the probability that 42 or more customers will choose company C's product, using the standard normal distribution table on the right? [3 points]

$Z$	$\mathrm { P } ( 0 \leqq Z \leqq z )$
0.5	0.1915
1.0	0.3413
1.5	0.4332
2.0	0.4772

(1) 0.6915
(2) 0.7745
(3) 0.8256
(4) 0.8332
(5) 0.8413

It is known that $10\%$ of the notebooks displayed in a certain stationery store are products from Company A. When a customer randomly purchases 100 notebooks from this store, find the probability that at least 13 notebooks from Company A are included using the standard normal distribution table below. [3 points]

$z$	$\mathrm { P } ( 0 \leqq Z \leqq z )$
0.75	0.2734
1.00	0.3413
1.25	0.3944
1.50	0.4332

(1) 0.0668
(2) 0.1056
(3) 0.1587
(4) 0.2266
(5) 0.2734

For a natural number $a$ not exceeding 6, a trial is performed using one die and one coin.
Roll the die once. If the result is less than or equal to $a$, flip the coin 5 times and record the number of heads. If the result is greater than $a$, flip the coin 3 times and record the number of heads.
This trial is repeated 19200 times, and let $X$ be the number of times the recorded number is 3. When $\mathrm { E } ( X ) = 4800$, find the value of $\mathrm { P } ( X \leq 4800 + 30 a )$ using the standard normal distribution table below, which equals $k$.

$z$	$\mathrm { P } ( 0 \leq Z \leq z )$
0.5	0.191
1.0	0.341
1.5	0.433
2.0	0.477
2.5	0.494
3.0	0.499

Find the value of $1000 \times k$. [4 points]