Homework Details:
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:
I. 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
|
a) Is this a normal distribution? Explain your reasoning.
b) What is an outlier? Are there any outliers in this distribution? Explain your reasoning fully.
c) Using the above data, what is the probability that the mean will be over 76 in any given July?
d) Using the above data, what is the probability that the mean will be over 80 in any given July?
II. 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
Format your homework according to the give formatting requirements:
a. The answer must be double spaced, typed, using Times New Roman font (size 12), with one-inch margins on all sides.
b. The response also includes a cover page containing the title of the homework, the course title, the student's name, and the date. The cover page is not included in the required page length.
c. Also include a reference page. The references and Citations should follow APA format. The reference page is not included in the required page length.