What property is being illustrated? The Empirical Rule Chebyshev's inequality ' ' The Law of Large Numbers The probability distribution of the random variable X represents the number of hits a baseball player obtained in a game for the 2012 baseball season. x 0 1 2 3 4 5 % P(x) 0.1679 0.3286 0.2802 0.1499 0.0384 0.0350 The probability distribution was used along with statistical software to simulate 25 repetitions of the experiment (25 games). The number of hits was recorded. Approximate the mean and standard deviation of the random variable X based on the simulation. The simulation was repeated by performing 50 repetitions of the experiment. Approximate the mean and standard deviation of the random variable. Compare your results to the theoretical mean and standard deviation. What property is being illustrated? Data Tables Table of the numbers of hits for 25 games 2 1 3 2 10 1 3 1 1 3 0 0 0 1 3 2 3 2 4 3 5 1 1 2 Table of the numbers of hits for 50 games 2 1 3 1 3 1 1 3 0 0 0 1 3 2 4 3 2 4 3 5 1 1 2 2 5 3 1 0 2 0 0 1 0 3 1 2 2 1 1 1 3 0 0 2 0 1 2Compute the theoretical mean of the random variable X for the given probability distribution. (Round to three decimal places as needed.) Compute the theoretical standard deviation of the random variable X for the given probability distribution. ox = - his (Round to three decimal places as needed.) Approximate the mean of the random variable X based on the simulation for 25 games. i w - hits (Round to three decimal places as needed.) Approximate the standard deviation of the random variable X based on the simulation for 25 games. 3% - hits (Round to three decimal places as needed.) Approximate the mean of the random variable X based on the simulation for 50 games. i z - hits (Round to three decimal places as needed.) Approximate the standard deviation of the random variable X based on the simulation for 50 games. 3 m - hits (Round to three decimal places as needed.) Compare these results to the theoretical mean and standard deviation. For the simulation for 25 games, the mean is the theoretical mean and the standard deviation is the theoretical standard deviation. For the simulation for 50 games, the mean is the theoretical mean and the standard deviation is the theoretical standard deviation