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 P(x)

0 0.1666

1 0.3278

2 0.2918

3 0.1492

4 0.0366

5 0.0280

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 beingillustrated?

Table of the numbers of hits for 25 games

2, 2, 3, 2, 1, 1

1, 1, 2, 0, 1, 1

2, 2, 0, 2, 2, 1

2, 3, 1, 3, 2, 2, 3

Table of the numbers of hits for 50 games

2, 2, 3, 2, 1, 1, 1

1, 2, 0, 1, 1, 2, 2

0, 2, 2, 1, 2, 3, 1

3, 2, 2, 3, 2, 2, 1

0, 0, 5, 0, 1, 2, 3

2, 1, 2, 1, 1, 4, 3,

1, 1, 3, 1, 1, 0, 1, 1

Compute the theoretical mean of the random variable X for the given probability distribution.

X= ___ hits

(Round to three decimal places asneeded.)