Standard Normal Distribution Probabilities
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Questions and Answers

What is the name of the plot that represents the probabilities of each possible outcome?

  • Histogram
  • Probability Distribution (correct)
  • Discrete Random Variable
  • Continuous Random Variable

    • What is the range of probability of each value of a discrete random variable?

  • 0 < P(x) < 1
  • 0 ≤ P(x) ≤ 1 (correct)
  • 0 ≤ P(x) < 1
  • 0 > P(x) > 1

    • What is the sum of the probabilities of all possible outcomes of a discrete random variable?

  • ∑ P(x) > 1
  • ∑ P(x) < 1
  • ∑ P(x) = 0
  • ∑ P(x) = 1 (correct)

    • What type of plot is used to visualize a discrete probability distribution?

    <p>Histogram</p> Signup and view all the answers

    What is an example of a discrete random variable?

    <p>The number of arrivals of aircraft at an airport</p> Signup and view all the answers

    What is the classification of the distribution of a continuous random variable?

    <p>Continuous probability distribution</p> Signup and view all the answers

    What is the x-axis of a histogram or probability distribution plot used to visualize a discrete probability distribution?

    <p>Outcome of the discrete variable</p> Signup and view all the answers

    What are two types of discrete random variables mentioned in the text?

    <p>Binomial and Hypergeometric</p> Signup and view all the answers

    Why did William Sealy Gossett publish his work under the pseudonym 'Student'?

    <p>To hide his identity from Guinness Brewery</p> Signup and view all the answers

    What is the primary method of communication for scholars to share information about statistical work?

    <p>Scholarly journals or academic conferences</p> Signup and view all the answers

    What is the name of the distribution that is defined by the degrees of freedom?

    <p>t-distribution</p> Signup and view all the answers

    What is the sum of a marginal probability distribution?

    <p>One</p> Signup and view all the answers

    What is the range of temperatures when it is said that the temperature is 39°C?

    <p>38.5°C to 39.5°C</p> Signup and view all the answers

    What is the significance of the degrees of freedom in statistical analysis?

    <p>It affects the precision and power of one's analyses</p> Signup and view all the answers

    What is used to describe a continuous probability distribution?

    <p>Probability density function</p> Signup and view all the answers

    How are conditional probability distributions obtained from a crosstab?

    <p>By dividing the cells of the crosstab by the row or column totals</p> Signup and view all the answers

    Who first introduced the concept of degrees of freedom in statistics?

    <p>Carl Frederick Gauss</p> Signup and view all the answers

    What type of calculus is used to find the area under the curve in a continuous probability distribution?

    <p>Integral calculus</p> Signup and view all the answers

    What is the purpose of a mean comparison test?

    <p>To detect the difference between two sample means or medians</p> Signup and view all the answers

    What is the characteristic shape of the t-distribution?

    <p>Bell-shaped with heavier tails</p> Signup and view all the answers

    What is the importance of hypothesis testing, which includes the use of t-tests?

    <p>It is regarded as one of the most important discoveries of the nineteenth century</p> Signup and view all the answers

    What is the most common type of continuous probability distribution?

    <p>Normal distribution</p> Signup and view all the answers

    What is the name of the nonparametric test used to compare medians?

    <p>Wilcoxon signed-rank test</p> Signup and view all the answers

    What is the main limitation of using sample means to make inferences about the population?

    <p>The sample mean can vary from the population due to random sampling error</p> Signup and view all the answers

    What is the purpose of the probability density function in a continuous probability distribution?

    <p>To represent the area under the curve</p> Signup and view all the answers

    What is the correct definition of degrees of freedom in applied statistics?

    <p>The number of independent values that can vary in your analysis without violating any constraints</p> Signup and view all the answers

    What is the purpose of studying the rules of crosstabulation tables?

    <p>To learn about the various rules and scenarios of crosstabulation tables</p> Signup and view all the answers

    What is a common scenario where a nonparametric test is used?

    <p>When the data is not normally distributed</p> Signup and view all the answers

    What is the purpose of the x-axis in a continuous probability distribution graph?

    <p>To represent the continuous random variable</p> Signup and view all the answers

    What is the primary purpose of the z-table?

    <p>To calculate the probability of randomly obtaining a score from the sample distribution</p> Signup and view all the answers

    What is the main concern when comparing two sample means or medians?

    <p>Deciding whether the difference is due to random error or a treatment effect</p> Signup and view all the answers

    What is the advantage of using a probability density function to describe a continuous probability distribution?

    <p>It provides a more precise representation of the distribution</p> Signup and view all the answers

    What is the percentage probability of randomly selecting a score between -2 and +2 standard deviations from the mean?

    <p>95.45%</p> Signup and view all the answers

    What is the primary difference between classical and quantum physics in terms of probability?

    <p>Classical physics views probability as an objective feature of reality, while quantum physics views it as a human construct</p> Signup and view all the answers

    What is the assumption of the classical probability method?

    <p>Every event has an equal likelihood of occurring</p> Signup and view all the answers

    What is the significance of the discovery of ancient societies playing probability games with primitive dice-like objects?

    <p>It demonstrates the universality of probability concepts across cultures</p> Signup and view all the answers

    What is the primary purpose of calculating probabilities in day-to-day life?

    <p>To make informed decisions in uncertain situations</p> Signup and view all the answers

    What is the name of the curve that represents the probabilities under the standard normal distribution?

    <p>Bell Curve</p> Signup and view all the answers

    What is the primary field of study that has changed our understanding of probability?

    <p>Quantum physics</p> Signup and view all the answers

    What is the defining characteristic of a continuous probability distribution?

    <p>It can take on any value within a certain range</p> Signup and view all the answers

    Study Notes

    Standard Normal Distribution

    • The z-table represents the probabilities under the standard normal distribution, allowing researchers to calculate the probability of randomly obtaining a score from the sample distribution.
    • There is a 95.45% probability of randomly selecting a score between -2 and +2 standard deviations from the mean.

    Probability Calculation

    • The study of probability began with ancient societies playing games with primitive dice-like objects made from animal bones.
    • Classical physics states that true probability exists due to unknown inputs, while quantum physics suggests that truly probabilistic phenomena exist at a subatomic perspective.
    • There are two methods of calculating probabilities: classical and non-classical.

    Classical Probability Method

    • In classical probability, every event has an equal likelihood of occurring.
    • Marginal probability distributions are provided by the row and column totals of a crosstab, with the sum of a marginal distribution being one.
    • Conditional probability distributions describe the distribution of one variable given the levels of the other variable, with the sum of a conditional distribution being one.

    Mean Comparison Test

    • A nonparametric test, such as the Wilcoxon signed-rank test, can be used to compare medians.
    • The probability distribution (PD) represents the probabilities of each possible outcome.
    • The height of each bar in the graph for X gives the probability of that particular outcome.

    Discrete Probability Distributions

    • A discrete probability distribution describes the distribution of a discrete random variable.
    • A discrete random variable is a variable resulting from an experiment with discrete or countable values.
    • Each value of a discrete random variable has a probability between zero and one, inclusive, and the sum of all probabilities is equal to one.
    • Discrete probability distributions can be visualized via a histogram or probability distribution plot.

    Continuous Probability Distributions

    • A continuous probability distribution is classified as such when the random variable is continuous.
    • Continuous probability distributions are expressed using a formula known as the probability density function.
    • The probability density function is used to find the area under the curve, which represents the probability.

    Normal Distribution

    • The normal distribution is the most common type of continuous probability distribution.
    • The t-distribution is defined by the degrees of freedom, which is a correction related to sample size.
    • The t-distribution is bell-shaped but has heavier tails than the standard normal distribution.

    Degrees of Freedom

    • The concept of degrees of freedom was first mentioned by Carl Frederick Gauss in the 1880s and was brought into modern statistics by William Sealy Gossett in the early 1900s.
    • Degrees of freedom are the number of independent values that can vary in an analysis without violating any constraints.
    • This concept is important in techniques such as the t-distribution and t-tests and can impact the precision and power of analyses.

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    Description

    This quiz focuses on understanding probabilities using the standard normal distribution, also known as the z-table, and calculating scores from sample distributions.

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