# STA 1625 Rasmussen College Es

Gaming and probability are intertwined. In fact, there is an entire discipline in mathematics called “Game Theory.” In this assessment, you will apply discrete and continuous probability distributions to games. There will be two parts: the first will concentrate on discrete probability distributions, and the second part will focus on continuous probability distributions.

##### Instructions
###### Part One – Data Table

The theoretical probability of rolling a fair six-sided die is 1/6 for any specific single outcome, such as rolling a one. You want to test the theoretical probability by running an experiment.

In this experiment, you need to roll a six-sided die 25 times. Record the outcome of each die roll. Create a discrete probability distribution using your outcomes as the probability. For example, if you rolled 4 fives out of your 25 total rolls, your probability would be 4/25.

• x – 1 – 2 – 3 – 4 – 5 – 6
• P(x)
###### Part Two – Discrete Probability Distribution

After filling in the table above with your experimental probability, answer the following questions. Show all work for full credit. Calculations should be performed in Excel while answers including an explanation of steps using proper terminology are provided in a separate document.

1. What is the expected outcome for rolling a six-sided die using the discrete probability distribution table above?

2. What is the probability of rolling an even number according to the discrete probability distribution table above?

• How does this compare to the theoretical probability of 0.5?
• Explain why you think there is a difference between the theoretical probability and the experimental probability you found.

3. Create a binomial probability distribution based on the discrete probability distribution table above where a success is rolling an even number. Answer the following questions:

• How do you know this is a Binomial Probability Distribution? Explain by showing how this example fits all four properties of a Binomial Probability Distribution.
• Define n,p,q.
• What is the probability that you will roll exactly 12 even numbers?
• What is the probability that you will roll at least 12 even numbers?
• Find the expected number of even numbers that you will roll.
###### Part Three – Continuous Probability Distribution

Dice are a common tool used in several board games. One board game which utilizes two dice is Monopoly. While the outcomes of rolling two dice in this game would be a discrete random variable, we are interested in looking at a continuous random variable associated with Monopoly and its respective probability.

The time it takes to finish a game of Monopoly is normally distributed with a mean of 120 minutes and a standard deviation of 30 minutes. Using this premise, answer the following questions. Show all work for full credit. Calculations should be performed in Excel while answers including an explanation of steps using proper terminology are provided in a separate document.

1. Explain why this is a continuous probability distribution instead of a discrete probability distribution.
2. What is the probability that a game lasts less than 45 minutes?
3. What is the probability that a game lasts more than 160 minutes?
4. What is the z-score of a game that lasts exactly 105 minutes?

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# STA 1625 Rasmussen College Es

Data can be collected from many different sources. In this assignment, you will perform a short survey of 10 people. From this data, you will create a frequency chart, histogram, and pie chart. You will also perform several statistical calculations.

##### Instructions
###### Part One – Survey Data

For this assignment, you will need to ask 10 people the following 5 questions and record their answers in an Excel spreadsheet:

• What is their first name?
• What is their age?
• Are they currently a student?
• How many hours of sleep do they average in a night?
• What is their favorite ice cream flavor?

Please Note: Some of the data collected will be used in the following module assignments. Make sure to ask all five questions and record all the data for each question.

###### Part Two – Graphs & Calculations

After you collect data from 10 people on the 5 questions above, complete the following in the same Excel spreadsheet used to collect the data:

• Create two frequency charts:
• The first frequency chart will be for their favorite ice cream flavor.
• The second frequency chart will be for their age and should contain between 5 and 10 class intervals.
• Create a histogram for age.
• Label the axes, title, and bars.
• Create a pie chart for favorite ice cream flavor.
• Label the key and percentage of each section.
• Calculate the following statistical values on the age variable:
• Measures of center – mean, median, mode, and midrange.
• Measures of variation – range and standard deviation.
###### Part Three – Presentation

After you have created your graphs and performed your calculations, create a presentation with the following information on each slide:

• Slide 1: Title slide with assignment title, name, course, date, instructor name.
• Slide 2: Provide a copy of the raw data in table format collected from 10 people.
• Slide 3: Copy and paste your two frequency charts.
• Slide 4: Copy and paste your histogram.
• What conclusions can you draw?
• Slide 5: Copy and paste your pie chart.
• What conclusions can you draw?
• Slide 6: Share the measures of center for age.
• Slide 7: Share the measures of variation for age.
• Slide 8: Conclusion – Summarize the data you collected.
• Were there any interesting outcomes you weren’t expecting?
• Was there any data that was helpful to draw further conclusions?
• What benefits did you gain from visualizing the data?
• What benefits did you gain from performing statistical calculations on the data?

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# STA 1625 Rasmussen College Es

You are recently hired at a sleep research company to perform statistical calculations. Your boss has assigned you two hypothesis tests to run.

Instructions

###### Part One – Hypothesis Tests

For the assignment, complete hypothesis tests of the two situations listed below by:

• Constructing an 8-step hypothesis test, showing all calculations,
• Including both the critical value method and the p-value method in your calculations.
• Using the correct terminology and interpretation of the resulting confidence interval for each test.
###### Hypothesis Test – Situation 1

It has been reported that the mean amount of sleep that adults receive is 7 hours per night. Your boss has asked you to look into this statistic by running your own study. You gather 49 adults and find the following information. The mean amount of sleep was 6.2 hours with a standard deviation of 1.8 hours. Based on your results, you claim that adults receive less than 7 hours of sleep. Test your claim with a 0.05 significance level.

###### Hypothesis Tests – Situation 2

Your boss also would like you to look at average sleep for a specific age range (between 35 and 44 years of age). It has been previously reported that 38.3% of adults in this age range receive the recommended amount of sleep per night (at least 7 hours). You decide to test this claim by gathering 32 adults between the ages of 35 and 44 years old. In the sample, you find that 15 of the participants receive at least 7 hours of sleep. Test the claim that more than 38.3% of adults get the recommended amount of sleep per night with a significance level of 0.01.

###### Part Two – Hypothesis Errors

After you have completed your hypothesis tests, in a separate paragraph,

• Explain the possible error(s) that could have occurred and what they imply for each test.
• Explain how you might prevent the error(s) from occurring in future hypothesis tests.

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# STA 1625 Rasmussen College Es

##### Overview

Statistics covers a wide range of topics from basic calculations of mean, median, and mode to finding the probability of a normal variable. In the last week of the course, review the concepts we have discussed and reflect on your experiences in this course.

##### Instructions

In your initial post, reflect on the following questions and provide explanations and examples:

• What concept(s) did you find to be the most enjoyable? Why?
• What concept(s) do you think will be most applicable in your future career path? Explain with examples.
• What concept(s) do you think will be most applicable in your everyday life? Explain with examples.

• Reflect on your peer’s post and identify any answers that you disagree with.
• Can you relate to any of the examples they provided?
• Or are there any other examples that your classmate may have missed in their reflection?
• Or reflect on the similarities and differences among your postings.