258 CHAPTER 6 Normal Probability Distributions Statistical Literacy and Critical Thinking 1.Normal Distribution What’s wrong with the following statement? “Because the digits 0, 1, 2, . . . , 9 are the normal results from lottery drawings, such randomly selected numbers have a normal distribution.” 2.Normal Distribution A normal distribution is informally described as a probability distribution that is “bell-shaped” when graphed. Draw a rough sketch of a curve having the bell shape that is characteristic of a normal distribution. 3.Standard Normal Distribution Identify the values of the mean and standard deviation for a normal distribution that is a standard normal distribution. 4. Notation What does the notation za indicate? Continuous Uniform Distribution. In Exercises 5–8, refer to the continuous uniform distribution depicted in Figure 6-2 and described in Example 1. Assume that a passenger is randomly selected, and find the probability that the waiting time is within the given range. 5. Greater than 3.00 minutes 6. Less than 4.00 minutes 7. Between 2 minutes and 3 minutes 8. Between 2.5 minutes and 4.5 minutes Standard Normal Distribution. In Exercises 9–12, find the area of the shaded region. The graph depicts the standard normal distribution of bone density scores with mean 0 and standard deviation 1. 9. z 5 0.44 10. z 521.04 11. z 520.84 z 5 1.28 12. z 521.07 z 5 0.67 Standard Normal Distribution. In Exercises 13–16, find the indicated z score. The graph depicts the standard normal distribution of bone density scores with mean 0 and standard deviation 1. 13. 0 0.8907 z 14. z 0 0.3050 6-1 Basic Skills and Concepts 0 0.2 1 2 Area 5 1 3 4 5 x (waiting time in minutes) P(x) FIGURE 6-2
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