Normal Distribution

• What is a normal distribution?

  A distribution that is symmetric about the mean
• What are the characteristics of a normal distribution?

  • Bell shaped and symmetric about the mean
  • Mean = median = mode
  • Total area under the curve is 1 or 100%
  • Long tapering tails that extend infinitely in either direction but never touch the x-axis
  • Completely determined by two parameters: mean (μ) and standard deviation (𝜎)
• What does the mean (μ) determine in a normal distribution?

  The location of the distribution
• What does the standard deviation (𝜎) determine in a normal distribution?

  The spread of the distribution
• What happens to the distribution when the standard deviation (𝜎) increases?

  The distribution becomes wider
• What happens to the distribution when the standard deviation (𝜎) decreases?

  The distribution becomes thinner
• What percentage of the distribution is covered by standard deviations?

  • 1 SD covers 68.25%
  • 2 SD covers 95.50%
  • 3 SD covers 99.75%
• What are the parameters of the standard normal distribution?

  Mean = 0 and standard deviation = 1
• What does the variable z represent in the context of the standard normal distribution?

  The number of standard deviations that falls above or below the mean
• How can any value x from the normal distribution be transformed into a standard normal value of z?

  Using the formula $z =$$\frac{x - \mu}{\sigma}$
• What are the steps to solve a normal distribution problem?

  1. Compute for the equivalent z value of the given x value
  2. Sketch the graph
  3. Get the area from the standard normal table
• How do you find the equivalent x value for the 1st quartile using the z value?

  Using the formula $x =$$z\sigma +$$\mu$