In: Statistics and Probability
In Unit 2, you have
learned about three different types of distributions: Normal,
binomial, and Poisson....
In Unit 2, you have
learned about three different types of distributions: Normal,
binomial, and Poisson. You can take data that you collect and plot
it out onto graphs to see a visual representation of the data. By
simply looking at data on a graph, you can tell a lot about how
related your observed data are and if they fit into a normal
distribution.
For this submission,
you will be given a series of scenarios and small collections of
data. You should plot the data or calculate probabilities using
excel. Then, you will create your own real or hypothetical scenario
to graph and explain.
Answer the
following:
- The mean temperature for the month of July in Boston,
Massachusetts is 73 degrees Fahrenheit. Plot the following data,
which represent the observed mean temperature in Boston over the
last 20 years:
1998 |
72 |
1999 |
69 |
2000 |
78 |
2001 |
70 |
2002 |
67 |
2003 |
74 |
2004 |
73 |
2005 |
65 |
2006 |
77 |
2007 |
71 |
2008 |
75 |
2009 |
68 |
2010 |
72 |
2011 |
77 |
2012 |
65 |
2013 |
79 |
2014 |
77 |
2015 |
78 |
2016 |
72 |
2017 |
74 |
- Is this a normal distribution? Explain your reasoning.
- What is an outlier? Are there any outliers in this
distribution? Explain your reasoning fully.
- Using the above data, what is the probability that the mean
will be over 76 in any given July?
- Using the above data, what is the probability that the mean
will be over 80 in any given July?
- A heatwave is defined as 3 or more days in a row with
a high temperature over 90 degrees Fahrenheit. Given the following
high temperatures recorded over a period of 20 days, what is the
probability that there will be a heatwave in the next 10 days?
Day 1 |
93 |
Day 2 |
88 |
Day 3 |
91 |
Day 4 |
86 |
Day 5 |
92 |
Day 6 |
91 |
Day 7 |
90 |
Day 8 |
88 |
Day 9 |
85 |
Day 10 |
91 |
Day 11 |
84 |
Day 12 |
86 |
Day 13 |
85 |
Day 14 |
90 |
Day 15 |
92 |
Day 16 |
89 |
Day 17 |
88 |
Day 18 |
90 |
Day 19 |
88 |
Day 20 |
90 |
Customer surveys
reveal that 40% of customers purchase products online versus in the
physical store location. Suppose that this business makes 12 sales
in a given day
- Does this situation fit the parameters for a binomial
distribution? Explain why or why not?
- Find the probability of the 12 sales on a given day exactly 4
are made online
- Find the probability of the 12 sales fewer than 6 are made
online
- Find the probability of the 12 sales more than 8 are made
online
Your own example:
- Choose a company that you have recently seen in the news
because it is having some sort of problem or scandal, and complete
the following:
- Discuss the situation, and describe how the company could use
distributions and probability statistics to learn more about how
the scandal could affect its business.
- If you were a business analyst for the company, what research
would you want to do, and what kind of data would you want to
collect to create a distribution?
- Would this be a standard, binomial, or Poisson distribution?
Why?
- List and discuss at least 3 questions that you would want to
create probabilities for (e.g., What is the chance that the company
loses 10% of its customers in the next year?).
- What would you hope to learn from calculating these
probabilities?
- Assuming that upper management does not see the value in
expending the time and money necessary to collect data to analyze,
make an argument (at least 100 words) convincing them that the
expenditure is necessary and explaining some dangers the company
could face by not knowing what the data predict.