Continuous Random Variables Chapter 5 Continuous Random Variables

Figure SIA5.1 Target placement on gun range Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Continuous Probability Distributions 5.1 Continuous Probability Distributions

Figure 5.1 A probability f(x) for a continuous random variable x Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Definition Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Figure 5.2 Density Function for Friction Coefficient, Example 5.1 Copyright © 2013 Pearson Education, Inc.. All rights reserved.

The Uniform Distribution 5.2 The Uniform Distribution

Figure 5.3 The uniform probability distribution Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Definition Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Figure 5.4 Distribution for x in Example 5.2 Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Figure 5. 5 Probability that car breaks down within 1 Figure 5.5 Probability that car breaks down within 1.5 months of purchase Copyright © 2013 Pearson Education, Inc.. All rights reserved.

The Normal Distribution 5.3 The Normal Distribution

Figure 5.6 A normal probability distribution Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Figure 5.7 Several normal distributions with different means and Standard deviations Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Procedure Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Figure 5.8 Several normal distributions: m = 0, s = 1 Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Definition Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Table 5.1 Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Figure 5.9 Areas under the standard normal curve for Example 5.3 Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Figure 5.10 Finding z =1.33 in the standard normal table, Example 5.3 Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Figure 5.11 Areas under the standard normal curve for Example 5.4 Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Figure 5.12 Areas under the standard normal curve for Example 5.5 Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Figure 5.13 Areas under the standard normal curve for Example 5.6 Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Definition Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Figure 5.14 Areas under the normal curve for Example 5.7 Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Procedure Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Figure 5.15 Area under the normal curve for Example 5.8 Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Figure 5.16 Area under the standard normal curve for Example 5.9 Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Figure 5.17 Areas under the standard normal curve for Example 5.10 Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Figure 5.18 Area under the normal curve for Example 5.11 Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Figure SIA5.2 MINITAB worksheet with cumulative normal probabilities Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Descriptive Methods for Assessing Normality 5.4 Descriptive Methods for Assessing Normality

Procedure Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Definition Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Table 5.2 Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Figure 5.19a MINITAB histogram for gas mileage data Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Figure 5.19b MINITAB Descriptive statistics for gas mileage data Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Figure 5.19c SPSS normal probability plot for gas mileage data Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Table 5.3 Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Table SIA5.1 Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Figure SIA5.3a MINITAB histogram for the horizontal hit measurements when s = 1 Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Figure SIA5.3b MINITAB histogram for the horizontal hit measurements when s = 2 Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Figure SIA5.3c MINITAB histogram for the horizontal hit measurements when s = 4 Copyright © 2013 Pearson Education, Inc.. All rights reserved.

5.5 Approximating a Binomial Distribution with a Normal Distribution (Optional)

Figure 5. 20 Binomial distribution for n = 20, p = Figure 5.20 Binomial distribution for n = 20, p = .6 and normal distribution with m = 12, s = 2.2 Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Figure 5.21 Rule of thumb for normal approximation to binomial probabilities Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Figure 5.22 Normal approximation to the binomial distribution with n = 200, p = .06 Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Figure 5.23 Standard normal distribution Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Procedure Copyright © 2013 Pearson Education, Inc.. All rights reserved.

The Exponential Distribution (Optional) 5.6 The Exponential Distribution (Optional)

Definition Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Figure 5.25 Exponential distributions Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Procedure Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Figure 5.27 Area to the right of a = 5 for Example 5.14 Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Figure 5.28 Area to the left of a = 5 for Example 5.15 Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Figure 5.29 Area in the interval for Example 5.15 Copyright © 2013 Pearson Education, Inc.. All rights reserved.