Continuous, Normal, and Standard Normal Probability Distributions

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# Continuous, Normal, and Standard Normal Probability Distributions - PowerPoint PPT Presentation

Continuous, Normal, and Standard Normal Probability Distributions. Sections 6.1, 6.2, &amp; 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

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
• Sum of all probabilities of intervals = 1
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
• Parameters are µ and σ.
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 the area (probability) to the left of z = 1.95
Example:
• Find the area (Probability) z = -2.17 to z = 0
Example:
• Find the area to the right of 2.32
Example:
• Find the area between -1.56 and 2.31.
• Check the Empirical Rule.