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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. 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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  1. Continuous, Normal, and Standard Normal Probability Distributions Sections 6.1, 6.2, & 6.3

  2. Continuous Random Variables • Not countable. • Examples: • Weights of babies. • Heights of women. • Amount paid for a house.

  3. Probability Histograms and Curves • 0 ≤ P(X) ≤ 1 • Sum of all probabilities of intervals = 1

  4. Probability of Intervals • P(X=65) =0

  5. 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.

  6. Normal Probability Curve • Parameters are µ and σ.

  7. Mean and Standard Deviation

  8. The Standard Normal Distribution • The mean = 0 and the standard deviation = 1. • Z-values or z-scores represent the values on the x-axis.

  9. Find probabilities under the standard normal distribution • Find the area (probability) to the left of z = 1.95

  10. Table IV in Appendix C

  11. Area (Probability)

  12. Example: • Find the area (Probability) z = -2.17 to z = 0

  13. Example: • Find the area to the right of 2.32

  14. Example: • Find the area between -1.56 and 2.31. • Check the Empirical Rule.

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