What are the proportions for the colors of M&M candy colors? You will need one Medium (approximately 12 ounce) bags of M&M’s. You may choose from any of the following varieties:

• • Peanut
• • Dark
• • Coconut
• • Almond
• • Crispy
• • Peanut Butter
• • Pretzel

Answer each of the questions below for your bags of candy in your project. Your final project should be in report form which includes the answers to the questions. The report should be typed. You may hand write neatly the mathematics symbols and your work. If you have any questions, you should contact your teacher.

1. A) Basics Information:

1. 1) Identify the colors of M&M’s that are in one of your packages. Be sure to indicate the variety of M&M and name the colors.
2. 2) Before you begin the data collection, state the percentages of colors that you think are in the bag. (2 points)
3. 3) Make a frequency distribution of the counts of the colors in your first bag and give the relative frequency for each color. (3 points)

4) The “color” of M&M is what type of data (two answers)? (1 point)

5) Graph the data by using an appropriate chart. (May use excel and paste the graph in the report). State why you chose you type of graph. (5 points)

B) Proportion test (you may use <, >, or ≠ for H₂):

Now, choose color. Just test one of the colors. Use the official proportion from M&M’s for p and compare to your proportion,. Use 5% for level of significance

1. 1) State the null and alternate hypotheses. (4 points)
2. 2) Find test stat and the P-value. (8 points)
3. 3) Sketch the sampling distribution and show the area corresponding to the P-value.(4 pts
4. 4) Will you reject or fail to reject the null hypotheses? State your conclusion in the context of the data. (9 points)

C) Good ness of fit

1) Do you think that the data you have gathered agrees with the company’s claims? (2 points)

2) Identify a procedure that you could use to check the goodness of fit for your data on one of the variety of M & M’s. (1 point)

3) Identify the H_o and H₁ you would use to verify the company’s claim. (4 points)

4) Display in a matrix the observed and expected cell values and perform a Chi-Square analysis for the one of M & M’s variety (10 points)

5) Write a word conclusion to the hypothesis test you have performed using the 1% level of significance. (Show all steps in your hypothesis test) (9 points)

D) Test for Independence

Now consider the type of M&M and the color. Use the one sample that you counted and one sample given to you (below) to test the hypothesis that the type of M&M is independent of the colors as listed.

1) Fill in your data in the chart below (3 points)

2) Filled in the expected amounts (6 points)

E = (Row total)(Column Total)/ Sample Size

3) Identify the H_o and H₁ you would use to verify the type of M&M is independent of the colors as listed.   

4) Perform a Chi-Square analysis for the two of M & M’s variety

5) Write a word conclusion to the hypothesis test you have performed using the 5% level of significance.   

Once you have the dataset, please use knowledge gained in other business and/or economics classes to realize what topic and theory the data could relate and a research question that it could allow you to answer. More specifically, please put together an analysis by making sure your project report includes the following:

1. Brief statement of the research topic and problem. As you get the dataset from me, you would need to use some imagination what research problem that data could be related to. Nevertheless, please state very briefly (i.e. in one paragraph) what theory (research literature or textbooks related to business or economics) says about the research problem – e.g. is there some dilemma or controversy that your research will help to clarify.
2. Clearly worded research question that limits the research problem to researchable task. (This is a short sentence that ends with the question mark and it is suggested that you draw from theory (research literature / textbook knowledge) in one of the business studies field to word it!)
3. Please identify the type of data that you are working with – on what type of measurement scale(s) where the selected variables measured by the original data collectors. (As you work with the dataset given by me, use your educated guess).
4. Describe the data with the tools of descriptive statistics, using both numerical as well as graphical methods. In addition to reporting and commenting on the values central tendency and diagrams, please also justify the choice of method (e.g. why a particular kind of measure of central tendency was selected and the chosen graphic is appropriate to use in this context).
5. Justify the selection of the specific data analysis method of inferential statistics. Recommendation – use the decision tree (introduced in Ch. 9ff) to make the selection and justification of it. You should look up also the assumptions and comment how your data meets them but I will not penalize you if it does not meet all the criteria. Nevertheless, please make sure that you include the basic information about distribution of the variables – are they more or less normally distributed (use both numerical as well as graphical methods). It is required that you restrict the choice of data analysis method(s) to the ones introduced in the class. (In addition to the fact that we covered only the most basic / frequently used methods in class, also the spreadsheet program (Excel) which the textbook is based on and that I presented during the course, has limited set of methods available).
6. Formulate the null and research (alternative) hypothesis – similarly to point 2 it is recommended that you word them on the basis of research literature / textbook knowledge in one of the business studies field that you know);
7. Determine the test criteria:

7.1. Specify the level of significance (Type I error associated with the null hypothesis),

7.2. Determine the test statistic (the appropriate statistical test as mentioned under point 5 above),

7.3. Determine the critical values (and region(s) if applicable),

8. Calculate the value of the test statistic (obtained value).
9. Make a decision about the null and research hypothesis by comparing the obtained value to the critical value and interpret the results of the data. You can pay attention also to the p-values.
10. Sum up you research report by relating the statistical test result(s) to the research question and theory that you set to test.

DATA :

This is a work integrated assessment item. The tasks are similar to what would be carried out in the workplace.

Tully Tyres sells cheap imported tyres. The manager believes its profits are in decline. You have just been hired as an analyst by the manager of Tully Tyres to investigate the expected profit over the next 12 months based on current data.

•Monthly demand varies from 100 to 200 tyres – probabilities shown in the partial section of the spreadsheet below, but you have to insert formulas to ge the cumulative probability distribution which can be used in Excel with the VLOOKUP command.
•The average selling price per tyre follows a discrete uniform distribution ranging from $160 to $180 each. This means that it can take on equally likely integer values between $160 and $180 – more on this below.
•The average profit margin per tyre after covering variable costs follows a continuous uniform distribution between 20% and 30% of the selling price.
•Fixed costs per month are $2000.

(a)Using Excel set up a model to simulate the next 12 months to determine the expected average monthly profit for the year. You need to have loaded the Analysis Toolpak Add-In to your version of Excel. You must keep the data separate from the model. The model should show only formulas, no numbers whatsoever except for the month number.

You can use this partial template to guide you:

The first random number (RN 1) is to simulate monthly demands for tyres.
•The average selling price follows a discrete uniform distribution and can be determined by the function =RANDBETWEEN(160,180) in this case. But of course you will not enter (160,180) but the data cell references where they are recorded.
•The second random number (RN 2) is used to help simulate the profit margin.
•The average profit margin follows a continuous uniform distribution ranging between 20% and 30% and can be determined by the formula =0.2+(0.3-0.2)*the second random number (RN 2). Again you do not enter 0.2 and 0.3 but the data cell references where they are located. Note that if the random number is high, say 1, then 0.3-0.2 becomes 1 and when added to 0.2 it becomes 0.3. If the random number is low, say 0, then 0.3-0.2 becomes zero and the profit margin becomes 0.2.
•Add the 12 monthly profit figures and then find the average monthly profit.

Show the data and the model in two printouts: (1) the results, and (2) the formulas. Both printouts must show the grid (ie., row and column numbers) and be copied from Excel and pasted into Word. See Spreadsheet Advice in Interact Resources for guidance.

(b)Provide the average monthly profit to Ajax Tyres over the 12-month period.

(c)You present your findings to the manager of Ajax Tyres. He thinks that with market forces he can increase the average selling price by $40 (ie from $200 to $220) without losing sales. However he does suggest that the profit margin would then increase from 22% to 32%.

He has suggested that you examine the effect of these changes and report the results to him. Change the data accordingly in your model to make the changes and paste the output in your Word answer then write a report to the manager explaining your conclusions with respect to his suggestions. Also mention any reservations you might have about the change in selling prices.

The report must be dated, addressed to the Manager and signed off by you.

Question 1:

Locate the Manufacturer tab. Test to determine if there is a significant difference between Mean Value Added by the manufacturer and the mean Cost of Materials in manufacturing assuming a 10% level of significance.

Must complete all the parts to this problem:

• PART 1: Use Excel to perform the Test for Equality of Variances. Copy and paste the output from Excel into a word document.
• PART 2: Write 1 – 2 sentences on the findings from the Test for Equality of Variances. Which two-sample t-test will be needed (equal variances or unequal variances)? Support your answer by using the output from the Test for Equality of Variances. You must include: the hypotheses for the F-test, a discussion of the p-value, and the decision you reach and why.
• PART 3: Run the test you chose in step 2 in Excel (t-test assuming equal variances or unequal variances) to test if there is a significant difference between Mean Value Added by the manufacturer and the mean Cost of Materials in manufacturing assuming a 10% level of significance. Copy and paste the output from Excel into a word document.
• PART 4: Write 3 - 4 sentences on the findings from the Two-sample T-test. Is there a significant difference between Mean Value Added by the manufacturer and the mean Cost of Materials in manufacturing assuming a 10% level of significance? Support your answer by using the output from the test. You must include: the hypotheses for the T-test, a discussion of the p-value, and the decision you reach and why.

Data: (Table was too large so I divided each data set into two columns)

Brainstorm a new type of health care technology that you believe would contribute to the health management information systems (HMIS) evolution. This technological advancement should either not yet exist or should serve to enhance existing technology to achieve an entirely new objective. What health care problems or challenges have you noticed for which there is not yet a solution? It is essential for health care administrators to be aware of the rapidly evolving and ever-changing field of health technology, both in terms of current as well as upcoming informational and system advancements. Assume that you are a health care administrator for an organization and you have been tasked with presenting this new technology to your organization's key stakeholders. After selecting your topic for this assignment, compose a 750-1,000-word proposal that addresses the following:

1. Describe your new HMIS technology and what purpose it will serve. Who will most benefit from it? What gap will it fill in the health care technology field? How will this technology improve the quality of health care that clinicians can offer?
2. What are the potential advantages and disadvantages of this HMIS technology for the consumer? In this case, the consumer is both the health care organization and the individual user or patient.
3. How will the use and integration of this technology impact digital equity in the HMIS field?
4. How will this technology collect, read, and interpret health data? Why and how will this data be useful to the health care organization?
5. From an administrative perspective, describe when, how, and where you propose this technology first be introduced, and discuss how you foresee it impacting the organization.

Describe your new HMIS technology and what purpose it will serve. Who will most benefit from it? What gap will it fill in the health care technology field? How will this technology improve the quality of health care that clinicians can offer?

What are the potential advantages and disadvantages of this HMIS technology for the consumer? In this case, the consumer is both the health care organization and the individual user or patient.

How will the use and integration of this technology impact digital equity in the HMIS field?

How will this technology collect, read, and interpret health data? Why and how will this data be useful to the health care organization?

From an administrative perspective, describe when, how, and where you propose this technology first be introduced, and discuss how you foresee it impacting the organization

Attached is our first individual project. Please reply to all 4 questions, including the subquestions: 1a, 1b, 1c, etc. What you should do is determine if the supply or demand will increase or decrease given the effect and then provide a real-life example..
For example; for question 1a, “Product B becomes more fashionable.”
   Answer: If product B becomes more fashionable. The demand curve will increase and shift to the right. A practical example is if there was an article in The New England Journal of Medicine; suggesting drinking a glass of orange juice will decrease heart disease. Presumably, orange juice will become more fashionable, causing demand to increase

Note – you should graph by using pencil and paper. I strongly urge you NOT to use Excel or related software, I don’t want you waste a lot of time as it is more important to understand the concept! Word is fine if use the drawing tools)

If you decided to graph, using Word, using Clip Art and Shapes, the demand shift for orange juice would look something like this

Thank you

1.   What effect will each of the following have on the demand for product B?
a.   Product B becomes more fashionable.
  
b.   The price of substitute product C falls.
  
c.   Income declines and product B is an inferior good.
  
d.   Consumers anticipate the price of B will be lower in the near future.
  
e.   The price of complementary product D falls.
  
f.   Foreign tariff barriers on B are eliminated.

2.   What effect will each of the following have on the supply of product B?
a.   A technological advance in the methods of producing B.
  
b.   A decline in the number of firms in industry B.
  
c.   An increase in the price of resources required in the production of B.
  
d.   The expectation that the equilibrium price of B will be lower in the future than it is currently.
  
e.   A decline in the price of product A, a good whose production requires substantially the same techniques as does the production of B.

f.   The levying of a specific sales tax upon B.
  
g.   The granting of a 50-cent per unit subsidy for each unit of B produced.

3.   How will each of the following changes in demand and/or supply affect equilibrium price and equilibrium quantity in a competitive market; that is do price and quantity rise, fall, remain unchanged, or are the answers indeterminate, depending on the magnitudes of the shifts in supply and demand? You should rely on a supply and demand diagram to verify answers.
a.   Supply decreases and demand remains constant.
  
b.   Demand decreases and supply remains constant.
  
c.   Supply increases and demand is constant.
  
d.   Demand increases and supply increases.
  
e.   Demand increases and supply is constant.
  
f.   Supply increases and demand decreases.
  
g.   Demand increases and supply decreases.
  

h. Demand decreases and supply decreases.
     

4.   Suppose the total demand for wheat and the total supply of wheat per month in the Kansas City grain market are as follows:

Thousands
of bushels
demanded   Price
per
bushel   Thousand
of bushels
Supplied   Surplus (+)
or
shortage (-)

85
80
75
70
65
60   $3.40
3.70
4.00
4.30
4.60
4.90   72
73
75
77
79
81  
   a.   What will be the market or equilibrium price? What is the equilibrium quantity? Using the surplus-shortage column, explain why your answers are correct.   
b.   Graph the demand for wheat and the supply of wheat. Be sure to label the axes of your graph correctly. Label equilibrium price “P” and the equilibrium quantity “Q.”
  

c.   Why will $3.40 not be the equilibrium price in this market? Why not $4.90? “Surpluses drive prices up; shortages drive them down.” Do you agree?

d   Now suppose that the government establishes a ceiling price of, say, $3.70 for wheat. Explain carefully the effects of this ceiling price.
   Demonstrate your answer graphically. What might prompt the government to establish a ceiling price

Difficult Transitions Tony had just finished his first week at Hotel Luxury Incorporated and decided to drive upstate to a small lakefront lodge for some fishing and relaxation. Tony had worked for the previous ten years for the Sun Group Company, but Sun Group had been through some hard times of late and had recently shut down several of its operating groups, including Tony’s, to cut costs. Fortunately, Tony’s experience and recommendations had made finding another position fairly easy. As he drove the interstate, he reflected on the past ten years and the apparent situation at Reece. At Sun Group , things had been great. Tony had been part of the team from day one. The job had met his personal goals and expectations perfectly, and Tony believed he had grown greatly as a person. His work was appreciated and recognized; he had received three promotions and many more pay increases. Tony had also liked the company itself. The firm was decentralized, allowing its managers considerable autonomy and freedom. The corporate Culture was easygoing. Communication was open. It seemed that everyone knew what was going on at all times, and if you didn’t know about something, it was easy to find out. The people had been another plus. Tony and three other managers went to lunch often and played golf every Saturday. They got along well both personally and professionally and truly worked together as a team. Their boss had been very supportive, giving them the help they needed but also staying out of the way and letting them work. When word about the shutdown came down, Tony was devastated. He was sure that nothing could replace Sun Group . After the final closing was announced, he spent only a few weeks looking around before he found a comparable position at the Luxury Hotel. As Tony drove, he reflected that "comparable" probably was the wrong word. Indeed, Luxury Hotel and Sun Group were about as different as you could get. Top managers at Luxury Hotel apparently didn’t worry too much about who did a good job and who didn’t. They seemed to promote and reward people based on how long they had been there and how well they played the never-ending political games. Maybe this stemmed from the organization itself, Tony pondered. Luxury Hotel was a bigger organization than Sun Group and was structured much more bureaucratically. It seemed that no one was allowed to make any sort of decision without getting three signatures from higher up. Those signatures, though, were hard to get. All the top managers usually were too busy to see anyone, and interoffice memos apparently had very low priority. Tony also had had some problems fitting in. His peers treated him with polite indifference. He sensed that a couple of them resented that he, an outsider, had been brought right in at their level after they had had to work themselves up the ladder. On Tuesday he had asked two colleagues about playing golf. They had politely declined, saying that they did not play often. But later in the week, he had overheard them making arrangements to play that very Saturday. It was at that point that Tony had decided to go fishing. As he steered his car off the interstate to get gas, he wondered if perhaps he had made a mistake in accepting the Luxury Hotel offer without finding out more about what he was getting into. Case Questions Task 1. Identify several concepts and characteristics from the field of organizational behavior that this case illustrates. Task 2. What advice can you give Tony? How would this advice be supuported or tempered by behavioral concepts and processes?

Part 1: Random Data, Statistics, and the Empirical Rule **Data Set Below**

Methods: Use Excel (or similar software) to create the tables and graph. Then copy the items and paste them into a Word document. The tables should be formatted vertically, have borders, and be given the labels and titles stated in the assignment. The proper symbols should be used. Do not submit this assignment as an Excel file. The completed assignment should be a Word (or .pdf) document.

1. The data values and relevant information are posted in the course website. Use the data set (P, Q, R, S, or T) assigned to you by your instructor to complete this application.

For the purpose of this application, treat the data set as if it represented a certain random variable and was a valid random sample gathered by a researcher from a normally distributed population. The sample data was actually found with an online Gaussian random number generator that creates normally distributed data values. The random number generator simulates the results of a researcher finding those values through observation or experimentation.

2. Use technology (Excel, graphing calculator, etc.) to sort the sample data values from low to high. Use Excel or similar software to put the data into a table with about 5 or 6 columns. Label this “Table 1: Sorted Set of Sample Data.”

3. Using 5 to 10 class intervals, organize the sample data as a frequency distribution in a table. The intervals of the frequency distribution should be rounded to the tenths so that they match the data. Label this “Table 2: Frequency Distribution.”

4. Use Excel (or similar software) to construct a frequency histogram to illustrate the data. Give the axes the proper titles. Label this “Graph 1: Histogram.”

5. Use Table 2, the frequency distribution, to find the midpoints of each class interval. Create a new frequency distribution with the midpoints in the left column and the frequencies in the right column. Label this “Table 3: Frequency Distribution with Midpoints.”

6. Use technology to find the mean, median, standard deviation, and variance of the sample data organized in Table 3 (from step 5 above). Put these values into a table with the proper symbol in the left column and the value of the statistic in the right column. Also, from the original data set, put the values of the range and sample size in the table. The median and range do not generally have symbols so the terms “Median” and “Range” can be used in the left column. Identify the modal class (the one with the highest frequency). Put the terms “Modal Class” in the left column and the class interval in the right column. The statistics should be rounded properly (one more decimal place than the data). Label this “Table 4: Summary Statistics”
7. Use the sample mean and standard deviation to find the values related to the Empirical Rule.

         The Empirical Rule: For a set of data whose distribution is approximately normal,

• about 68% of the data are within one standard deviation of the mean.
• about 95% of the data are within two standard deviations of the mean.
• about 99.7% of the data are within three standard deviations of the mean.

Use the value of n and the percents listed above to find how many data values should be within each category. Then use the sample mean and standard deviation to find the lower and upper cut-off values in each category. Then use the sorted list of data to determine how many values are actually in each category. Put the values into a table as shown in the example and label it “Table 5: The Empirical Rule.”

(Side note: I'm not sure if this counts as one question or not but all questions are based on the original case and numbers and felt as splitting the questions would be counter-productive)

Case: A small convenience store chain is interested in modeling the weekly sales of a store, y, as a function of the weekly traffic flow on the street where the store is located. The table below contains data collected from 20 stores in the chain.

1. [3 marks] Create a scatter plot of weekly sales (y) vs. traffic flow (x) using MS Excel. Copy and paste (or save and import) your plot to Word. Provide horizontal and vertical axis labels, including appropriate units, and give your plot a title. Based on your plot, do you think there is a linear relationship between the two variables? Why or why not? Answer in a single sentence.

2. [7 marks]

a) [1 mark] State the equation of the fitted regression line between weekly sales and traffic flow. No need to show your work calculating the coefficients – you may use Excel for this; however, make sure you use Word’s equation editor to type the equation properly. Please round the coefficients to 2 decimal places.

b) [1 mark] In one sentence, interpret the value of the fitted y-intercept in question 2.

c) [1 mark] In one sentence, interpret the value of the fitted slope in question 2.

d) [1 mark] What is the coefficient of determination for the fitted model? Again, you may use Excel for this, no need to show your work. Please round to 3 decimal places.

e) [1 mark] In one sentence, interpret the value of the coefficient of determination.

f) [2 marks] The chain wants to establish a new store at a location where the weekly traffic flow is 64,500 cars. Use the fitted equation to predict the weekly sales of the planned store. Show your work and explain what the result means in a single sentence.

3. [6 marks] Use a hypothesis test on the population slope to determine if there is a significant linear relationship between weekly sales and traffic flow. Provide all five steps as shown in class.

1) The null and alternative hypotheses:


2) The test statistic (yes, you may copy/paste from Excel, but please round to 3 decimal places):


3) The critical value(s) is/are:

4) Do you reject the null hypotheses? (Answer Yes or No): _________

5) Interpret.

4. [5 marks] Use an ANOVA F-test to determine if there is a significant linear relationship between weekly sales and traffic flow. No need to show calculations for the test statistic here; provide only the final answer. Provide all five steps as shown in class.

1) The null and alternative hypotheses:



2) The test statistic (yes, you may copy/paste from Excel, but please round to 3 decimal places):

3) The p-value (yes, you may copy/paste from Excel, but please provide 4 significant digits):

4) Do you reject the null hypotheses? (Answer Yes or No): _______.

5) Interpret.

5. [4 marks] Create a residual plot. Copy and paste (or save and import) your plot to Word. You may use the default axis titles and overall title provided by Excel. In one sentence, comment on whether the assumption of constant variance is satisfied. In one sentence, comment on whether the assumption of zero mean is satisfied.

I. Consider the random experiment of rolling a pair of dice. Note: Write ALL probabilities as reduced fractions or whole numbers (no decimals).

1) One possible outcome of this experiment is 5-2 (the first die comes up 5 and the second die comes up 2). Write out the rest of the sample space for this experiment below by completing the pattern:

2) How many outcomes does the sample space contain? _____________

3) Draw a circle (or shape) around each of the following events (like you would to circle a word in a word search puzzle). Label each event in the sample space with the corresponding letter. Event A has been done for you.

A: Roll a sum of 3.
B: Roll a sum of 7.
C: Roll a sum of at least 10.

D: Roll doubles.
E: Roll snake eyes (two 1’s). F: First die is a 4.

4) Find the following probabilities:
P(A) = _________ P(B) = _________ P(C) = _________

P(D) = _________ P(E) = _________ P(F) = _________

5) The conditional probability of B given A, denoted by P(B|A), is the probability that B will occur when A has already occurred. Use the sample space above (not a special rule) to find the following conditional probabilities:

P(D|C) = _________ P(E|D) = _________ P(D|E) = _________ P(A|B) = _________ P(C|F) = _________

6) Two events are mutually exclusive if they have no outcomes in common, so they cannot both occur at the same time.

Are C and E mutually exclusive? ___________
Find the probability of rolling a sum of at least 10 and snake eyes on the same roll, using the

sample space (not a special rule).
P(C and E) = __________

Find the probability of rolling a sum of at least 10 or snake eyes, using the sample space. P(C or E) = __________

7) Special case of Addition Rule: If A and B are mutually exclusive events, then P(A or B) = P(A) + P(B)

Use this rule to verify your last answer in #6:
P(C or E) = P(C) + P(E) = ________ + ________ = _________

8) Are C and F mutually exclusive? __________ Using sample space, P(C or F) = _________ 9) Find the probability of rolling a “4” on the first die and getting a sum of 10 or more, using the

sample space.
P (C and F) = ________

10) General case of Addition Rule: P(A or B) = P(A) + P(B) – P(A and B) Use this rule to verify your last answer in #8:

P(C or F) = P(C) + P(F) – P(C and F) = ________ + ________ − ________ = _________

11) Two events are independent if the occurrence of one does not influence the probability of the other occurring. In other words, A and B are independent if P(A|B) = P(A) or if P(B|A) = P(B).

Compare P(D|C) to P(D), using the sample space: P(D|C) = ________ . P(D) = ________ .
Are D and C independent? _________
When a gambler rolls at least 10, is she more or less likely to roll doubles than usual? ___________ Compare P(C|F) to P(C), using the sample space: P(C|F) = ________ . P(C) = ________ .

Are C and F independent? __________
12) Special case of Multiplication Rule: If A and B are independent, then P(A and B) = P(A) · P(B).

Use this rule to verify your answer to #9:
P(C and F) = P(C) • P(F) = ________ · ________ = ________ .

13) Find the probability of rolling a sum of at least 10 and getting doubles, using the sample space. P(C and D) = ________ .

14) General case of Multiplication Rule: P(A and B) = P(A) · P(B|A). Use this rule to verify your answer to #13:

P(C and D) = P(C) • P(D|C) = ________ · ________ = ________ .