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11.(a)1220.920.90DPPPµµ.(b)222218.104.22.1688DVVV´´.(c)±²±²6 or620.880.3789.DDP xxP z!³ µ!12.(a)Geometric probability:±² ±²40.840.160.0797(b) Binomial probability:±²±²5binomcdf 10,0.84,50.0130P Xd.(c)From part (b), f the soccer player’s success rate were still 84%, the probability that he wouldscore 5 or few goals in 10 penalty kicks is 0.0130.This is so low that we should be suspiciousabout whether he can still hit 84% of his shots.We have convincing evidence that his penaltykick success rate has fallen below 84%.