250 CHAPTER 6 Normal Probability Distributions The following examples illustrate procedures that can be used with real and important applications introduced in the following sections. TABLE 6-1 Formats Used for Finding Normal Distribution Areas Cumulative Area from the Left The following provide the cumulative area from the left up to a vertical line above a specific value of z: • Table A-2 • Statdisk • Minitab • Excel • StatCrunch z Cumulative Left Region Area Between Two Boundaries The following provide the area bounded on the left and bounded on the right by vertical lines above specific values. • TI-83, 84 Plus calculator • StatCrunch Upper Lower Area Between Two Boundaries CAUTION When working with a normal distribution, be careful to avoid confusion between z scores and areas. ROUND-OFF RULE FOR z SCORES Round z scores to two decimal places, such as 2.31. (Table A-2 includes z scores rounded to two decimal places.) Bone Density Test EXAMPLE 3 A bone mineral density test can be helpful in identifying the presence or susceptibility to osteoporosis, a disease that causes bones to become more fragile and more likely to break. The result of a bone density test is commonly measured as a z score. The population of z scores is normally distributed with a mean of 0 and a standard deviation of 1, so these test results meet the requirements of a standard normal distribution, and the graph of the bone density test scores is as shown in Figure 6-5. A randomly selected adult undergoes a bone density test. Find the probability that this person has a bone density test score less than 1.27. SOLUTION Note that the following are the same (because of the aforementioned correspondence between probability and area): ■ Probability that the bone density test score is less than 1.27 ■ Shaded area shown in Figure 6-5 So we need to find the area in Figure 6-5 below z = 1.27. If using technology, see the Tech Center instructions included at the end of this section. If using Table A-2, begin with the z score of 1.27 by locating 1.2 in the left column; next find the value TA C T t Go Figure 134: The number of times people check their smartphones every day, according to a Dignity Health survey of 2000 smartphone users.
RkJQdWJsaXNoZXIy NjM5ODQ=