What is Normal Distribution Discussion Question; From the e-Activitity

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Mathematics

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From the e-Activity, discuss whether or not the winning history of the team you selected follows a normal distribution. Provide a rationale to support your response.

Go to the baseball reference Website, located at http://www.baseball-reference.com/teams/, select a baseball team from the list of teams, and analyze the team’s historical win percentage

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Explanation & Answer

Here is my answer :)

What is Normal Distribution Discussion Question;
From the e-Activitity
From the e-Activity, discuss whether or not the winning history of the team you selected
follows a normal distribution. Provide a rationale to support your response.
Go to the baseball reference Website, located at http://www.baseball-reference.com/teams/,
select a baseball team from the list of teams, and analyze the team’s historical win percentage.

The baseball team that was selected from the list of teams was Cincinnati Reds.
Firstly, we need to know what are the conditions where a data set follows a normal
distribution:
-

Skewness & kurtosis z-value should be somewhere in the span of -1.96 to +1.96
Histograms should visually indicate that our data are approximately normally
distributed.
Plot a Probability Density Function and see if it has a bell shape.

Using excel was calculated the descriptive statistics which include the skewness and
kurtosis values.
Descriptive Statistics
Mean
Standard Error
Median
Mode
Standard Deviation
Sample Variance
Kurtosis
Skewness
Range
Minimum
Maximum
Sum
Count
Confidence Level (95.0%)

76.88970588
1.040763545
76
76
12.13728433
147.313671
-0.59592362
0.162880075
56
52
108
10457
136
2.058310026

The Skewness & Kurtosis values are 0.1629 and -0.5959 respectively and these values are
between -1.96 and +1.96.

A histogram was constructed to see if it is symmetrical and approximately normally
distributed.

We can observe that the histogram is not at all symmetrical but it is a good approximation.
A probability density function was developed where the Y-axis is the normal probability
function and X-axis are the games won.

Also, it was developed normal probability plot and the coefficient of determination was R2 =0.9773
and the correlation coefficient is R = 0.9886 which represent a strong linear relationship.

Normal Probability Plot
120
y = 0.5018x + 39.071
R² = 0.9773

Sample Quantity

100
80
60
40
20
0
0

20

40

60

80

100

120

140

Theoretical Quantity

Conclusion:
After perform the analysis we can conclude that the winning history of the Cincinnati Reds

team is normally distributed. It is not a perfect dataset but it’s a good approximation.


What is Normal Distribution Discussion Question;
From the e-Activitity
From the e-Activity, discuss whether or not the winning history of the team you selected
follows a normal distribution. Provide a rationale to support your response.
Go to the baseball reference Website, located at http://www.baseball-reference.com/teams/,
select a baseball team from the list of teams, and analyze the team’s historical win percentage.

The baseball team that was selected from the list of teams was Cincinnati Reds.
Firstly, we need to know what are the conditions where a data set follows a normal
distribution:
-

Skewness & kurtosis z-value should be somewhere in the span of -1.96 to +1.96
Histograms should visually indicate that our data are approximately normally
distributed.
Plot a Probability Density Function and see if it has a bell shape.

Using excel was calculated the descriptive statistics which include the skewness and
kurtosis values.
Descriptive Statistics
Mean
Standard Error
Median
Mode
Standard Deviation
Sample Variance
Kurtosis
Skewness
Range
Minimum
Maximum
Sum
Count
Confidence Level (95.0%)

76.88970588
1.040763545
76
76
12.13728433
147.313671
-0.59592362
0.162880075
56
52
108
10457
136
2.058310026

The Skewness & Kurtosis values are 0.1629 and -0.5959 respectively and these values are
between -1.96 and +1.96.

A histogram was constructed to see if it is symmetrical and approximately normally
distributed.

We can observe that the histogram is not at all symmetrical but it is a good approximation.
A probability density function was developed where the Y-axis is the normal probability
function and X-axis are the games won.

Also, it was developed normal probability plot and the coefficient of determination was R2 =0.9773
and the correlation coefficient is R = 0.9886 which represent a strong linear relationship.

Normal Probability Plot
120
y = 0.5018x + 39.071
R² = 0.9773

Sample Quantity

100
80
60
40
20
0
0

20

40

60

80

100

120

140

Theoretical Quantity

Conclusion:
After perform the analysis we can conclude that the winning history of the Cincinnati Reds

team is normally distributed. It is not a perfect dataset but it’s a good approximation.


Year

Tm

Lg

2017
2016
2015
2014
2013
2012
2011
2010
2009
2008
2007
2006
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
1995
1994
1993
1992
1991
1990
1989
1988
1987
1986
1985
1984
1983
1982
1981
1980
1979
1978
1977
1976
1975
1974
1973
1972

Cincinnati RedsNL Central
Cincinnati RedsNL Central
Cincinnati RedsNL Central
Cincinnati RedsNL Central
Cincinnati RedsNL Central
Cincinnati RedsNL Central
Cincinnati RedsNL Central
Cincinnati RedsNL Central
Cincinnati RedsNL Central
Cincinnati RedsNL Central
Cincinnati RedsNL Central
Cincinnati RedsNL Central
Cincinnati RedsNL Central
Cincinnati RedsNL Central
Cincinnati RedsNL Central
Cincinnati RedsNL Central
Cincinnati RedsNL Central
Cincinnati RedsNL Central
Cincinnati RedsNL Central
Cincinnati RedsNL Central
Cincinnati RedsNL Central
Cincinnati RedsNL Central
Cincinnati RedsNL Central
Cincinnati RedsNL Central
Cincinnati RedsNL West
Cincinnati RedsNL West
Cincinnati RedsNL West
Cincinnati RedsNL West
Cincinnati RedsNL West
Cincinnati RedsNL West
Cincinnati RedsNL West
Cincinnati RedsNL West
Cincinnati RedsNL West
Cincinnati RedsNL West
Cincinnati RedsNL West
Cincinnati RedsNL West
Cincinnati RedsNL West
Cincinnati RedsNL West
Cincinnati RedsNL West
Cincinnati RedsNL West
Cincinnati RedsNL West
Cincinnati RedsNL West
Cincinnati RedsNL West
Cincinnati RedsNL West
Cincinnati RedsNL West
Cincinnati RedsNL West

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