Question

9. The probability distribution of the random variable X reoresents the number of hits a baseball plaver obtained in a aame for the 2012 baseball season.

x	0	1	2	3	4	5
P(x)	0.1667	0.3382	0.2856	0.1486	0.0381	0.0228

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 theoretical mean and standard deviation. What property is being illustrated?

1 Click the icon to view the data tables.

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

μX=_______  1.622 _______  hits

(Round to three decimal places as needed.)

σx=_______  1.170 hits

(Round to three decimal places as needed.)

Approximate the mean of the random variable X based on the simulation for 25 games.

x̅ ≈ hits

(Round to three decimal places as needed.)

Approximate the standard deviation of the random variable X based on the simulation for 25 games.

s ≈ hits

(Round to three decimal places as needed.)

Approximate the mean of the random variable X based on the simulation for 50 games.

x̅ ≈ hits

(Round to three decimal places as needed.)

Approximate the standard deviation of the random variable X based on the simulation for 50 games,

s ≈ hits

(Round to three decimal places as needed.)

For the simulation for 25 games, the mean is (1), the theoretical mean and the standard deviation is (2). the theoretical standard deviation. For the simulation for 50 games, the mean is (3), the theoretical mean and the standard deviation is (4). the theoretical standard deviation. What property is being illustrated?

The Empirical Rule

The Law of Large Numbers

Chebyshev's inequality

1: Data Tables

Table of the numbers of hits for 25 games

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

Table of the numbers of hits for  50  games 

2	2	1	1	1	3	0	1	0	2
1	2	1	3	2	3	2	3	1	0
3	2	1	3	3	0	1	3	1	3
3	2	1	1	1	2	1	1	2	1
1	1	0	1	4	1	1	4	1	1

Answer 1