MAT201: Probability Report

This report details a student's analysis of their daily television viewing time using probability concepts. The student collected data over ten days, calculating the average viewing time and the probability of watching television for at least 70 minutes daily. Two datasets were compared: one collected by the student and another provided by their parents. The report contrasts experimental and theoretical probability, highlighting the differences in predictions based on the two datasets. The student discusses the impact of an outlier (a day with significantly less viewing time due to an unexpected guest) on the data and its effect on the calculated probabilities. The report concludes by emphasizing the differences between experimental and theoretical probability and how they can lead to varying predictions. References to relevant statistics textbooks are included.

Introduction to Probability 1
Introduction to Probability
Laura Peña-Duval
MAT201 / Basic Statistic
April 20, 2017
Professor Qian Liu

Introduction to Probability 2
The data collection will be based on the time I spend watching television. To record the time, a
stopwatch will be used. I usually watch television in the evening time, so once I begin watch
television, I will start the stopwatch and annotate the minutes I spend in front of the television.
This collection of data is random in nature because it was not collected purposely. I do watch
television daily, and hence there is no predisposition associated with the data set. However, in
the evening time I do not wait for a certain time to begin watching television. I watch certain
sitcoms and shows that I record due to conflict of schedules.
The data collected for ten days is as shown in the below table:
Day1 73 Minutes
Day2 80 Minutes
Day3 65 Minutes
Day4 20 Minutes
Day5 69 Minutes
Day6 75 Minutes
Day7 72 Minutes
Day8 73 Minutes
Day9 68 Minutes
Day10 70 Minutes
The average of these ten days TV watching time is calculated as below:

Introduction to Probability 3
Therefore, on an average 66.5 minutes are spent to watching television every day. In this data,
the minutes are independent variables because this can be changed independently while making
the experiment and day a controlled variable because there are only 24 hours in a day hence it is
fixed.
Let’s calculate the probability that I watch television at least 70 minutes every day. Since there
are six days on which I watched television more than 70 minutes it will be used for calculation as
shown below:
This means that there is a 60% chance, I will watch television at least 70 minutes every day. This
collection of data and calculating probabilities shows that it is an experimental probability case
because we are trying to experiment with the television watching habits to make predictions
about this behavior. However, if we expect something to happen without any calculation, for
example, the probability which is calculated from the provided data is referred to as the
theoretical probability case since it does not have any prior calculation to make a judgment.
Now suppose the data is provided by my parents as shown below:
Day1 70 Minutes
Day2 80 Minutes
Day3 86 Minutes

Introduction to Probability 4
Day4 72 Minutes
Day5 69 Minutes
Day6 76 Minutes
Day7 78 Minutes
Day8 74 Minutes
Day9 83 Minutes
Day10 85 Minutes
Again, calculate the probability that I watch television at least 70 Minutes every day. Since, there
are nine days on which I watched TV more than 70 Minutes will be used for calculation as
shown below:
It means that there is a 90% chance, I will watch television at least 70 minutes every day. The
probability calculated on the basis of data collected by me makes a prediction of watching
television 70 minutes or more everyday has a 60% chance. The probability calculated on the
basis of data given by my parents makes a prediction of watching the television 70 minutes or
more every day has an 90% chance. As you can see, there is a big difference between these two
predictions because theoretical probabilities are based on the events which are calculated by
using our own expectations while experimental probabilities are calculated by performing those
events which shows that of what happens in reality. Sometimes these probabilities are very close
to each other.

Introduction to Probability 5
The data collected by me for five days have one day with 20 minutes that is an infrequent and
occurred because a guest came to my home in the evening, cutting into my time short. This
unexpected visit made the data a bit skewed.

Introduction to Probability 6
References
Bluman, Allan. G.(2009), Elementary Statistics. New York, NY: McGraw-Hill
Mann, Prem S.(2012), Introductory Statistics. New Jersey, NJ: John Wiley & Sons, Inc.
Rumsey, Deborah(2010), Statistics Essentials for Dummies. New Jersey, NJ: John Wiley &
Sons, Inc.