(12 points)
To compare the yields of an old and a new breeding method, a survey was conducted on 100 aquaculture farms, recording the yield (in kg) of a certain aquatic product. The frequency distribution histogram is given.
(1) Let $A$ denote the event ``the yield using the old breeding method is less than 50 kg''. Estimate the probability of $A$.
(2) Complete the contingency table below, and use the chi-squared test to determine whether we can be 99\% confident that yield is related to breeding method.

	Yield $< 50 \text{ kg}$	Yield $\geq 50 \text{ kg}$
Old breeding method
New breeding method

$P(K^2 \geq k)$	0.050	0.010	0.001
$k$	3.841	6.635	10.828

$$K^2 = \frac{n(ad - bc)^2}{(a+b)(c+d)(a+c)(b+d)}$$

17. (12 points) Two machine tools, A and B, produce the same type of product. Products are classified by quality into first-grade and second-grade products. To compare the quality of products from the two machine tools, 200 products were produced by each machine tool. The quality statistics are shown in the table below:

	First-grade	Second-grade	Total
Machine A	150	50	200
Machine B	120	80	200
Total	270	130	400

(1) What are the proportions of first-grade products produced by machine A and machine B respectively?
(2) Can we conclude with 99\% confidence that there is a difference in product quality between machine A and machine B? Attachment: $k^2 = \frac{n(ac - bd)^2}{(a+b)(c+d)(a+c)(b+d)}$,

$P(K^2 \geq k)$	0.050	0.010	0.001
$k$	3.841	6.635	10.828