Five people were randomly selected,
Sampling rate k=540= 18
The number of viewers over 40 years old should be 24× 18=3 (name) ... (3 points) (2 points in the formula, 1 minute).
(2) According to the data in the contingency table,
K2 = 100× (40× 24？ 16× 20) 256× 44× 60× 40 =1600 231≈ 6.926 > 6.635 ... (7 points)
(Formula 2 points, calculate 1 minute, and judge 1 minute)
Therefore, it is 99% sure that the audience watching cultural festivals is related to their age ... (8 points)
(3) The possible value of ξ is 0, 1, 2,3 ... (9 points)
p(ξ= 0)= c 3 12c 320 = 1 157，
p(ξ= 1)= c 18c 2 12c 320 = 4495，
p(ξ= 2)= c28c 1 12c 320 = 2895，
P (ξ = 3) = C38C320 =14285 ... (11min) (0.5 points each, rounded off).
Distribution list of ξ is
ξ 0123p1157 4495 289514285 ... (12 points)
ξ e = 0×1157+1× 4495+2× 2895+3× mathematical expectation.