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.

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