Assignment Details

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

  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?

  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

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

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 the

The following data is provided for the S&P 500 Index:

Refer to the information above. Calculate the 20-year arithmetic average annual rate of return on the S&P 500 Index.

Question 22 options:

The following table provides the Dow Jones Industrial Average (DJIA) opening index value on the first working day of 1991–2010:

YEAR DJIA YEAR 2 DJIA

2010 10,431 2000 11,502

2009 8,772 1999 9,213

2008 13,262 1998 7,908

2007 12,460 1997 6,448

2006 10,718 1996 5,117

2005 10,784 1995 3,834

2004 10,453 1994 3,754

2003 8,342 1993 3,301

2002 10,022 1992 3,169

2001 10,791 1991 2,634

• Develop a trend line and use it to predict the opening DJIA index value for years 2011, 2012, and 2013. Find the MSE for this model.

Alternative-Fueled Vehicles The table shows the numbers (in thousands) of alternative-fueled

vehicles A in use in the United States from 1995 to 2011. (Source: U.S. Energy Information Administration)

(a) Use a graphing utility to plot the data. Let t represent the year, with t = 5 corresponding to 1995. (b) A model for the data is

4615.36t − 8726.7

1 + 15.01t − 0.542t2, 5 ≤ t ≤ 21

where t = 5 corresponds to 1995. Use the model to estimate the numbers of alternative-fueled vehicles in 1996, 2006, and 2011. How do your answers compare to the original data?

(f ) Use the model to predict the numbers of alternative-fueled vehicles in 2016 and 2017

* Need help to understand F . Should I be using a particular formula

Plot the data on air travel delays. Can you see seasonal patterns? Explain. Use Megastat to calculate estimated seasonal indices and trend. Which months have the most delays? The fewest? Is this logical? Is there a trend in the deseasonalized data?

The balance on services for year 2007 is​ (in millions) ​$ ----- (Round to the nearest integer and enter any deficit with a negative​ sign.)

The balance on services for year 2008 is​ (in millions) ​$ ----- ​(Round to the nearest integer and enter any deficit with a negative​ sign.)

The balance on services for year 2011 is​ (in millions) ​$ ----- ​(Round to the nearest integer and enter any deficit with a negative​ sign.)

Energy consumed in the US can be classified ascoming from one of three sources: fossil fuels, nuclear power, andrenewable energy. In 2014, the energy from these three sourceswas 80.3, 8.3, and 9.6 quadrillion BTU, respectively. In 2004, thecorresponding amounts were 85.8, 8.2, and 6.1. Write a descriptionof the changes from 2004 to 2014 expressed in these data. Illustrateyour summary with appropriate graphical summaries. Be sure todiscuss both the amounts of energy from each source as well as thepercents.

An equally weighted portfolio consists of 74 assets which all have a standard deviation of 0.252. The average covariance between the assets is 0.091. Compute the standard deviation of this portfolio. Please enter your answer as a percentage to three decimal places (i.e. 12.345% rather than 0.12345 -- the percent sign is optional).

Suppose a geyser has a mean time between eruptions of 74 minutes74 minutes. Let the interval of time between the eruptions be normally distributed with standard deviation 28 minutes28 minutes. What is the probability that a randomly selected time interval between eruptions is longer than 86 minutes? (b) What is the probability that a random sample of 15 time intervals between eruptions has a mean longer than 86 minutes? (c) What is the probability that a random sample of 32 time intervals between eruptions has a mean longer than 86 minutes? What effect does increasing the sample size have on the probability? Provide an explanation for this result. Fill in the blanks below. If the population mean is less than 8686 minutes, then the probability that the sample mean of the time between eruptions is greater than 8686 minutes ▼ decreases increases because the variability in the sample mean ▼ decreases increases as the sample size ▼ decreases. increases. (e) What might you conclude if a random sample of 32 time intervals between eruptions has a mean longer than 86 minutes? Select all that apply. A. The population mean is 74 , and this is just a rare sampling. B. The population mean must be more than 74 , since the probability is so low. C. The population mean may be less than 74. D. The population mean is 74 , and this is an example of a typical sampling result. E. The population mean may be greater than 74. F. The population mean cannot be 74 , since the probability is so low. G. The population mean must be less than 74, since the probability is so low.

During June, the following changes in inventory item 27 took place:

Perpetual inventories are maintained.

What is the cost of the ending inventory for item 27 under the FIFO method?

Cost of the ending Inventory?