School FC are said to have a 30% chance of winning any football match. They have 10 matches in a season. 1. What statistical distribution would you use to model this? 2. Define the distribution 3. What is the probability that School FC win 5 matches?

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1 Properties of the Distribution are: Set number of trials - 10 in the seasonFixed ProbabilitySuccess or Failure (Win or not Win)All independent of each otherTherefore, only distribution that fits is binomial.2 X~B(n,p) where n [index]= number of trials = 10, p[parameter] = probability of success = 30%=0.3Therefore X~B(20,0.3)3 P(X=a) = (n!)/(a!x((n-a)!))pa(1-p)(n-a)Therefore, P(X=5)=[(10!)/((5!)x(5!))] x 0.35x (1 - 0.3)(10-5) = 252 x 0.00243 x 0.16807 = 0.103 (3sf)

Finn C.

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