Question

A volunteer for the local running club counted the number of participants at each race. Number of participants Number of races 21 74 3 142 3 165 1 1 182 1 - 189 1 X is the number of participants that a randomly chosen race had. What is the expected value of X? Write your answer as a decimal.

Answer 1

No of participants(xi) No of races Probability(p(x)) p(x)xi

21 1 0.1 2.1

74 3 0.3 22.2

142 3 0.3 42.6

165 1 0.1 16.5

182 1 0.1 18.2

189 1 0.1 18.9

Total = 10

The expected value= sum of p(x)xi = 2.1+ 22.2+42.6+16.5+18.2+18.9=120.5