5.87 Marks per round in cricket. Cricket is a dart game that uses the numbers 15 to 20 and the bull’s-eye. Each time you hit one of these regions, you score either 0, 1, 2 or 3 marks. Thus, in a round of three throws, a person can score 0 to 9 marks. Lex plans to play 20 games. Her distribution of marks per round is discrete and strongly skewed. A majority of her rounds result in 0, 1, or 2 marks and only a few are more than 4 marks. Assume that her mean is 2.07 marks per round with a standard deviation of 2.11.
(a) Her 20 games involve 140 rounds of three throws each. What are the mean and standard deviation of the average number of marks in 140 rounds?
(b) Using the central limit theorem, what is the probability that she averages fewer than 2 marks per round?
(c) Do you think that the central limit theorem can be used in this setting? Explain your answer.