Since watchingQueen's GambitBarbara has become slightly addicted to online chess. Over the last year she has played a total of 142 games. The frequency of different numbers of games per week is shown below: there were 5 weeks when she played no games, 6 where she played one game, and so on.

a)[1 mark]The mean games/ week has been smudged out. What value should it be?

b)[2 marks]What assumptions would need to hold for the number of games played per week to follow a Poisson distribution?

c)[1 mark]What formula was used to calculate the value in cell C2?

d)[1 mark]What formula was used to calculate the value in cell D2?

e)[3 marks]The p-value has also been smudged out. Give a formula to evaluate the p-value, calculate it, and interpret what it means.

A B C D E Number of Poisson Expected 1 games/week Frequency Probability Frequency (0 - E)^2/E 2 0 5 0.07 3.39 0.77 3 1 6 0.18 9.25 1.14 4 11 0.24 12.64 0.21 W N un 10 0.22 11.50 0.20 4 16 0.15 7.85 8.46 5 4 0.14 7.37 1.54 8 #weeks 52 chi^2 statistic 12.31 10 total games 142 p-value mean 11 games/week