Normal Distribution Probability Density Function
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Questions and Answers

What is the parameter representing the mean or expectation of the normal distribution?

  • $rac{1}{ u}$
  • $rac{1}{ heta}$
  • $rac{1}{ ext{μ}}$ (correct)
  • $rac{1}{eta}$
  • Which theorem states that the average of many samples of a random variable with finite mean and variance converges to a normal distribution?

  • Law of large numbers
  • Pythagorean theorem
  • Bayes' theorem
  • Central limit theorem (correct)
  • What is the variance of a normal distribution with standard deviation $ ext{σ}$?

  • $rac{1}{2 ext{σ}}$
  • $ ext{σ}^2$ (correct)
  • $rac{1}{ ext{σ}^2}$
  • $2 ext{σ}$
  • What type of distribution is often used to represent real-valued random variables in natural and social sciences?

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

    What does the parameter $ ext{σ}$ represent in the normal distribution?

    <p>$ ext{Standard deviation}$</p> Signup and view all the answers

    What is the formula for calculating the standard score (z-score) of a raw score?

    <p>$z = \frac{x - \mu}{\sigma}$</p> Signup and view all the answers

    What type of scores have positive standard scores according to the standard score definition?

    <p>Raw scores above the mean</p> Signup and view all the answers

    What is another common term used interchangeably with 'standard score'?

    <p>z-score</p> Signup and view all the answers

    When computing a z-score with only a sample of observations, what should be used instead of the population parameters?

    <p>Sample mean and sample standard deviation</p> Signup and view all the answers

    What does a negative z-score indicate about a raw score in relation to the mean?

    <p>The raw score is below the mean</p> Signup and view all the answers

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