Continuous normal and standard normal probability distributions
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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

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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


Probability of intervals

Probability of Intervals

  • P(X=65) =0


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.


Mean and standard deviation

Mean and Standard Deviation


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


Table iv in appendix c

Table IV in Appendix C


Area probability

Area (Probability)


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.


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