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Continuous, Normal, and Standard Normal Probability Distributions. Sections 6.1, 6.2, & 6.3. Continuous Random Variables. Not countable. Examples: Weights of babies. Heights of women. Amount paid for a house. Probability Histograms and Curves. 0 ≤ P(X) ≤ 1

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continuous normal and standard normal probability distributions

Continuous, Normal, and Standard Normal Probability Distributions

Sections 6.1, 6.2, & 6.3

continuous random variables
Continuous Random Variables
  • Not countable.
  • Examples:
    • Weights of babies.
    • Heights of women.
    • Amount paid for a house.
probability histograms and curves
Probability Histograms and Curves
  • 0 ≤ P(X) ≤ 1
  • Sum of all probabilities of intervals = 1
the normal distribution
The Normal Distribution
  • Many natural random phenomenon have normal distributions.
  • Bell-shaped.
  • Area under curve = 1.
  • Curve is symmetric about the mean.
  • Tails extend indefinitely.
normal probability curve
Normal Probability Curve
  • Parameters are µ and σ.
the standard normal distribution
The Standard Normal Distribution
  • The mean = 0 and the standard deviation = 1.
  • Z-values or z-scores represent the values on the x-axis.
find probabilities under the standard normal distribution
Find probabilities under the standard normal distribution
  • Find the area (probability) to the left of z = 1.95
example
Example:
  • Find the area (Probability) z = -2.17 to z = 0
example1
Example:
  • Find the area to the right of 2.32
example2
Example:
  • Find the area between -1.56 and 2.31.
  • Check the Empirical Rule.