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 (D)</p> Signup and view all the answers

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

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

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

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

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

<p>z-score (A)</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 (B)</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 (C)</p> Signup and view all the answers

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