Category: Mathematics Homework Help

Probability Report Worksheet

Directions: Complete the probability report worksheet to help you with your calculations to create the APA report.

1. Choose one of the three scenarios:

• Probability of obtaining heads on a coin toss
• Probability of rolling a 2 on a 6-sided die. 
• Probability of drawing a Jack from a deck of cards. 

2. Calculate the theoretical probability for your chosen scenario. Show all work! Remember probability is the number of ways you can achieve the desired outcomes divided by the total number of outcomes.  Then calculate the theoretical probability of your chosen scenario NOT happening. Ex: What is the probability of “Not Heads”? What is the probability of “Not rolling a 2”, etc.

3. Complete 100 trials for your chosen scenario. Example: Flip a coin 100 times and record the outcome, roll a die 100 times and record the outcome, choose a card from a deck (with replacement) 100 times.

4. Create a table in Microsoft Word here and record your data.

5. Using the table you created in number 4, what is the experimental probability for your chosen scenario?

6. Using the table you created in number 4, what is the experimental probability for NOT achieving your chosen scenario? Example: What is the probability of “Not Heads”? What is the probability of “Not rolling a 2”, and so on.

7. Does your theoretical probability match your experimental probability? 

8. Complete research on WHY your probabilities might not match or why they might match. *Be sure to cite your source*

9. Using the concepts learned this week, what do you think would happen if you did 1,000 trials? *Be sure to cite your reading or lecture*

Assignment Instructions

M7 Assignment: Probability

Probability Report

The probability of an event can be determined in theory as well as in practice. In this project, you will use the formulas and methods in your readings to determine the theoretical probability. You will then conduct an experiment to see if the outcomes match what you expect to find with the theoretical probability.

In this project you will:

1. be able to calculate and interpret probability
2. be able to analyze and compare theoretical and experimental probabilities

To complete this project you will:

1. Complete the Probability Report Worksheet to guide you in writing your APA report. Be sure to show all work!
2. Complete a 2-page, double-spaced, APA-formatted report. In the report you need to present your findings and explain your conclusions on experimental and theoretical probability.  Thoughts to include in the report include: How are theoretical and experimental probability different? Why might the theoretical probability not match the experimental probability?

Research has shown that people whose foot length to height ratio is greater than .15 are less likely to tip over than those whose ratio is not.

1. In cell J1 write an english sentence starting with the word if that describes how to classify a person as either “tippy” or “stable”.
2. Add a column to the data that classifies each entry as either “Stable” or “Tippy”. Your entries must include the use of the IF function.

1. We dene a sequence (an), n in N recursively by

a_1 = -2 and a_(n+1) = -sqrt( 4 -a_n)

Note that (an) n in N is well-defined and we have an < 0 for all n in N

A. Show that (an), n in N is decreasing and bounded below.

Hint: Show that -3 < an+1 < an, for all n in N by induction.

B. Show that (an) n in N converges. Moreover, compute lim n->oo. You can use part 1, even if you did not solve it.

2.Let (an) n in N be a bounded sequence. We set L = lim sup( an); l = lim inf (an):

A. Show that L; l belong to R.

B. Show that for all ϵ > 0, there exists n0 belong to N such that for all n > n0, we have l – ϵ < an < L + ϵ: You can use part 1, even if you did not solve it. Hint: Use the definition of lim sup; sup; lim inf; inf.

3.Let (an) n in N be a sequence such that lim n->oo (an) = 0: Show that for every ϵ > 0, there exists a subsequence (an(k)) k belong to N such that the series Σ1 {k=1,oo} an(k) converges and |Σ1{k=1,oo} an(k)| < ϵ: Hint: Show that there exists 0 < r < 1 such that Σ1{n=1,oo} rn = r/(1-r) < ϵ: Then construct appropriate (n(k)) k belong to N inductively.

4.Let (an) n in N, (bn) n in N be sequences such that |an+1 – an| < bn

for all n in N and the series Σ1{n=1,oo} bn converges. Show that THE SEQUENCE (an) n in N converges.

5.Dene a function f : R {0} -> R by f(x) =( x^2 – 1)/x

Show that f is continuous on the domain using the ϵ- g denition of continuity. For this problem, it is forbidden to use results on continuity from the textbook and lectures.

This assignment will assess your ability to apply the concepts of chapter 10 to conduct simple and multiple regression analyses to create a prediction model from data for a random sample of 1,000 houses located in the greater Wilmington, DE area (attached file Data File.xlsx) You will calculate various descriptive statistics, create summary tables, create various charts and develop five regression prediction models. Finally, you will create a written report summarizing your findings. You will need to use the Data Analysis ToolPak Add-in as you did in the previous two case studies.

Please refer to the video on how to run regression analysis in Excel (Links to an external site.). The video demonstrates multiple regression. To perform a simple regression, just the column for one independent variable instead of multiple columns.

Details of the assignment are contained in the document (attached file – Regression Model.docx)

Reference

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