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

12/12/2017 Section 6.1 Homework­Clayton Leach

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9.

Student: Clayton Leach Date: 12/12/17

Instructor: Ralph Leon Course: Math 110 Fall 2017 Assignment: Section 6.1 Homework

1: Data Tables

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) 0.1668 0.3340 0.2810 0.1483 0.0377 0.0322

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? Click the icon to view the data tables.1

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

hitsμX = 1.653 (Round to three decimal places as needed.)

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

hitsσX = 1.212 (Round to three decimal places as needed.)

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

hitsx = (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.

hitsx = (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.)

Compare these results.

As the number of independent repetitions of the experiment increases, the difference between and , the mean of the discrete random variable X, approaches .

x μX

What property is being illustrated?

The Law of Large Numbers The Empirical Rule Chebyshev's inequality

Table of the numbers of hits for 25 games

12/12/2017 Section 6.1 Homework­Clayton Leach

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0 2 2 1 5 2 0 1 1 1 1 1 0 4 1 2 0 3 3 2 3 2 3 2 0

Table of the numbers of hits for 50 games

0 2 2 1 5 2 0 1 1 1 1 1 0 4 1 2 0 3 3 2 3 2 3 2 0 2 0 2 0 1 1 3 1 1 1 3 1 1 2 3 2 2 0 3 5 3 2 0 0 1