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 2.21 marks per round, with a standard deviation of 1.90, and that her 20 games will involve 140 rounds.

Questions:

A) What are the mean and standard deviation of the average number of marks x̄ in 140 rounds?

Have part solved: Mean = x̄ = μ = 2.21

B) Using the central limit theorem, what is the probability that Lex averages fewer than 2 marks per round?

C) Do you think that the probability obtained in part (b) is a good approximation to the true probability in this setting? Explain your answer.

Please show work to solve please! Not looking to solve with statistics programs/calculators.