It is thought that the number of goals scored in a sports match can be modelled by a Poisson distribution. To test this theory the number of goals in 50 games was collected and the data is shown in the table below. Goals 0 1 2 3 4 4 5 26 Frequency 7 10 11 10 6 4 2 It is known that the average number of goals per game over a season is 2.4. a Taking the mean as 2.4 and assuming a Poisson distribution, calculate the missing entries in the table below. Goals 0 1 2 3 4 5 6 Probability Expected frequency b Use a hypothesis test at the 10% signi- ficance level to test whether the number of goals scored in a game follows a Poisson distribution with a mean of 2.4.