(1) According to the meaning of the question, the score is (0.02+0.032+a+0.018) ×10 =1,…( 1).

The answer is a = 0.03...(2 points)

(2) The average weight of 50 particle samples is

. X = 0.2×10+0.32× 20+0.3× 30+0.18× 40 = 24.6 (g) ... (3 points)

Estimating the population from the sample, it can be estimated that the average weight of the balls in the box is about 24.6 grams ... (4 points).

(3) Using samples to estimate the population, the probability that the weight of the ball in the box is within (5, 15) is 0.2.

Then ξ ~ b (3, 15)...(5 points)

The value of zeta is 0, 1, 2, 3, ... (6 points).

P(ξ=0)=C03(45)3=64 125，

p(ξ= 1)= c 13( 15)(45)2 = 48 125，

p(ξ= 2)= C23( 15)2(45)= 12 125，

p(ξ= 3)= C33( 15)3 = 1 125...( 10)

The list of ∴ξdistribution is:

ξ0 1 23p 64 125 48 125 125 125 1 125...( 1 1)

∴eξ= 0×64 125+ 1×48 125+2× 12 125 = 35 ...