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Chapter 6 Continuous Probability Distributions
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Chapter 6 Continuous Probability Distributions. Figure 6.1 A Discrete Probability Distribution. Probability is represented by the height of the bar. P( x ). 1 2 3 4 5 6 7 x. Holes or breaks between values. f ( x ). - PowerPoint PPT Presentation

### Transcript of Chapter 6 Continuous Probability Distributions

• Chapter 6

Continuous Probability Distributions

• Figure 6.1 A Discrete Probability Distribution Probability is represented by the height of the bar.Holes or breaks between values 1 2 3 4 5 6 7 xP(x)

• Figure 6.2 A Continuous Probability Distribution

• Figure 6.3 Marias Commute Time Distribution

• Figure 6.4 Computing P(64 < x < 67) Probability = Area = Width x Height = 3 x 1/20 = .15 or 15%

• Figure 6.5 Total Area = 1.0 1/20

• Uniform Probability Density Function (6.1) f(x) =1/(b-a) for a < x < b0 everywhere else

• Figure 6.7 The Bell-Shaped Normal Distribution Mean is mStandard Deviation is sx

• Normal Probability Density Function (6.5) f(x) =

• Normal Distribution PropertiesApproximately 68.3% of the values in a normal distribution will be within one standard deviation of the distribution mean, m.

Approximately 95.5% of the values in a normal distribution will be within two standard deviations of the distribution mean, m.

Approximately 99.7% of the values (nearly all of them) in a normal distribution will be found within three standard deviations of the distribution mean, m.

• Figure 6.8 Normal Area for m + 1s

• Figure 6.9 Normal Area for m + 2s m-2s m m+2s

• Figure 6.10 Normal Area for m + 3s

• Standard Normal Table

• Normal Table (2)

• Normal Table (3)

• Normal Table (4)

• Figure 6.11 Area in a Standard Normal Distribution for a z of +1.2 0 1.2 z.3849

• z-score Calculation (6.6) z =

• Figure 6.12 P(50 < x < 55)

• Figure 6.13 P(x > 58) 50 58 x (diameter) .4772 0 2.0 zm =50s = 4.0228

• Figure 6.14 P(47 < x < 56)

• Figure 6.15 P(54 < x < 58)

• Figure 6.16 Finding the z score for an Area of .25 0 ? z.2500

• Exponential Probability (6.7) Density Function f(x) =

• Figure 6.17 Exponential Probability Density Function f(x) =l/elxf(x)x

• Calculating Area for the (6.8) Exponential Distribution P(x > a) =

• Figure 6.18 Calculating Areas for the Exponential Distribution

• Figure 6.19 Finding P(1.0 < x < 1.5)

• Figure 6.20 Finding P(1.0 < x < 1.5)

• Expected Value for the (6.9) Exponential Distribution E(x) =

• Variance for the Exponential (6.10) Distribution 2s2 =

• Standard Deviation for the (6.11) Exponential Distribution s = =