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Category: Probability

  • Title: Probability of Drawing Balls from a Jar

    A jar contains 10 red balls, 15 blue balls, and 5 green balls. If you randomly draw 3 balls from the jar without replacement, what is the probability that you will draw:
    a) All three balls of the same color?
    b) Exactly two balls of the same color and one of a different color? c) One ball of each color?

  • Title: Calculating the Probability of Drawing Two Consecutive Red Cards from a Standard Deck

    What is the probability of drawing two red cards consecutively from a standard deck of cards without replacement? show all calculation.

  • Title: The Pitfalls of Self-Reported Data Collection Self-reported data refers to information that is provided by individuals about themselves, typically through surveys or questionnaires. This type of data collection is often used in research studies, market research,

    Explain why using self-reported data instead of measured data is a potential pitfall in data collection. Be sure to include an example.

  • “Probability of Drawing Two Specific Colored Marbles from a Bag without Replacement”

    “Suppose you have a bag containing 5 red marbles, 3 blue marbles, and 2 green marbles. You randomly select two marbles from the bag without replacement. What is the probability that the first marble drawn is red and the second marble drawn is blue?”

  • Title: Analyzing the “Freshman 15” Phenomenon: A Statistical Study of Weight Changes in College Students

    Many college students are familiar with the term “Freshman 15” which is referring to the average 15-pound (6.8 Kg) weight gain that students my incur during their first year in college. The reasons students may gain weight will vary. Certainly, a change in eating habits, lack of exercise, long hours of studying and being sedentary, stress and anxiety are just a few examples of what can cause weight gain. For this activity, you will use a dataset to evaluate before and after weights for both males and females by conducting summary statistics, graphing your data, and drawing some overall conclusions based on your analysis. Instructions
    Part I:
    Conduct this activity in MyLab by PearsonSummary Statistics: Select “Content” from the Brightspace Navigation toolbar. Select “MyLab Statistics” from the “Content” menu.
    Click on the “MTH 210 StatCrunch” tab
    Click on “Open Link”
    Select the “StatCrunch Website”
    Under the Data Column > select “Data Sets”
    Search for the data set “Freshman_15” and select the data Analyze your data using the Stat pull-down menu:Stat> Summary Stats> Columns
    Click “WT SEPT” to move to the right panel
    In “Group by”, select “Sex” from drop down menu
    Select “Compute!” At the bottom right.
    Copy and paste your results into a word document
    Repeat the steps above just selecting for b. “WT APRIL” and copy and paste your results into the same word document. Summary statistics for WT SEPT:
    Group by: SEX
    SEX
    n
    Mean
    Variance
    Std. dev.
    Std. err.
    Median
    Range
    Min
    Max
    Q1
    Q3
    F
    35
    58.057143
    40.467227
    6.3613856
    1.0752704
    57
    28
    42
    70
    54
    63
    M
    32
    72.71875
    110.85383
    10.528715
    1.8612314
    71
    43
    54
    97
    65.5
    76
    Summary statistics for WT APRIL:
    Group by: SEX
    SEX
    n
    Mean
    Variance
    Std. dev.
    Std. err.
    Median
    Range
    Min
    Max
    Q1
    Q3
    F
    35
    59.257143
    34.373109
    5.8628585
    0.99100395
    58
    22
    47
    69
    56
    64
    M
    32
    73.875
    118.17742
    10.870944
    1.9217295
    71
    50
    55
    105
    68
    82
    Graphs: You may choose histograms (1) or boxplots (2) to represent your data. If you choose histograms, you will create 4 graphs: WT SEPT Female, WT SEPT Male, WT APRIL Female and WT APRIL Male. If you choose boxplots, both genders can be represented in the same display for a total of 2 graphs for both months. Histograms (4 graphs total)Graph > Histogram
    Click “WT SEPT” to move to the right panel (repeat all steps again for “WT APRIL”)
    In “Group by”, select “Sex” from drop down menu Select markers (mean and median)
    Select “Compute” At the bottom right.
    Copy and paste your graphs into a word document (there will be one for F and one for M as you arrow over in your results)
    Boxplots (2 graphs total)Graph>Boxplots
    Click “WT SEPT” to move to the right panel (repeat all steps again for “WT APRIL”)
    In “Group by”, select “Sex” from drop down menu
    Select markers (mean and median)
    Hit Compute! At the bottom right. Part II: Interpretation and Conclusions
    Answer the following questions in the submission box below:Use your knowledge from Module 1 to discuss the following: How did the average weights change from September to April for males and for females?
    Look at the median. Was there a significant shift between the months for males and females?
    Describe the shape of the distributions of the graphs for both genders. Were there any potential outliers causing skewness in the data for either month?
    Give your overall conclusions based on your analytical results. In this dataset, does it appear that gaining 15 lbs (6.8 Kg) on average is accurate over this time frame (a statistically significant change)? Explain.