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.

• 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:
1. Is this a normal distribution? Explain your reasoning.
2. What is an outlier? Are there any outliers in this distribution? Explain your reasoning fully.
3. Using the above data, what is the probability that the mean will be over 76 in any given July?
4. 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?

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

1. Does this situation fit the parameters for a binomial distribution? Explain why or why not?
2. Find the probability of the 12 sales on a given day exactly 4 are made online
3. Find the probability of the 12 sales fewer than 6 are made online
4. Find the probability of the 12 sales more than 8 are made online

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

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