copyright © 2013 pearson education, inc. all rights reserved chapter 5 continuous random variables

Copyright © 2013 Pearson Education, Inc. All rights reserved

Chapter 5

Continuous Random Variables

5 - 2 Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Figure SIA5.1 Target placement on gun range


5.1

Continuous Probability Distributions


Figure 5.1 A probability f(x) for a continuous random variable x


Definition


Figure 5.2 Density Function for Friction Coefficient, Example 5.1


5.2

The Uniform Distribution


Figure 5.3 The uniform probability distribution


Definition


Figure 5.4 Distribution for x in Example 5.2


Figure 5.5 Probability that car breaks down within 1.5 months of purchase


5.3

The Normal Distribution


Figure 5.6 A normal probability distribution


Figure 5.7 Several normal distributions with different means and Standard deviations


Procedure


Figure 5.8 Several normal distributions: 01


Definition


Table 5.1


Figure 5.9 Areas under the standard normal curve for Example 5.3


Figure 5.10 Finding z =1.33 in the standard normal table, Example 5.3


Definition


Figure 5.14 Areas under the normal curve for Example 5.7


Procedure


Figure 5.15 Area under the normal curve for Example 5.8


Figure 5.16 Area under the standard normal curve for Example 5.9


Figure 5.18 Area under the normal curve for Example 5.11


Figure SIA5.2 MINITAB worksheet with cumulative normal probabilities


5.4

Descriptive Methods for Assessing Normality


Procedure


Definition


Table 5.2


Figure 5.19a MINITAB histogram for gas mileage data


Figure 5.19b MINITAB Descriptive statistics for gas mileage data


Figure 5.19c SPSS normal probability plot for gas mileage data


Table 5.3


Table SIA5.1


Figure SIA5.3a MINITAB histogram for the horizontal hit measurements when


Figure SIA5.3b MINITAB histogram for the horizontal hit measurements when


Figure SIA5.3c MINITAB histogram for the horizontal hit measurements when


5.5

Approximating a Binomial Distribution with a Normal Distribution (Optional)


Figure 5.20 Binomial distribution for n= 20, p = .6 and normal distribution with = 12,


Figure 5.21 Rule of thumb for normal approximation to binomial probabilities


Figure 5.22 Normal approximation to the binomial distribution with n = 200, p = .06


Figure 5.23 Standard normal distribution


Procedure


The Exponential Distribution (Optional)

5.6


Definition


Figure 5.25 Exponential distributions


Procedure


Figure 5.27 Area to the right of a = 5 for Example 5.14


Figure 5.28 Area to the left of a = 5 for Example 5.15


Figure 5.29 Area in the interval for Example 5.15

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copyright © 2013 pearson education, inc. all rights reserved chapter 5 continuous random variables

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