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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, & 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

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

• Sum of all probabilities of intervals = 1

• P(X=65) =0

### 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.