302 Chapter 7 The Normal Distribution EXAMPLE 7.14 Finding an area under a normal curve by using technology In Example 7.13, we used Table A.2 to compute the proportion of pregnancies that last longer than 280 days. Find this proportion by using technology. Solution We present output from the TI-84 Plus calculator. We use the normalcdf command. We enter the left endpoint of the interval (280). Since there is no right endpoint, we enter 1E99, which represents the very large number that is written with a 1 followed by 99 zeros. Then we enter the mean (272) and the standard deviation (9). Step-by-step instructions are given in the Using Technology section on page 305. Explain It Again Technology and tables can give slightly different answers: Answers obtained with technology sometimes differ slightly from those obtained by using tables, because the technology is more precise. The differences aren’t large enough to matter. In Example 7.13, we used Table A.2 and found the proportion of pregnancies that last longer than 280 days to be 0.1867. In Example 7.14, the TI-84 Plus calculator found the proportion to be 0.1870. Answers found with technology often differ somewhat from those obtained by using a table. The differences aren’t large enough to matter. Whenever the answer obtained from technology differs from the answer obtained by using the table, we will present both answers. EXAMPLE 7.15 Finding an area under a normal curve between two values The length of a pregnancy from conception to birth is approximately normally distributed with mean �� = 272 days and standard deviation �� = 9 days.Apregnancy is considered fullterm if it lasts between 252 days and 298 days. What proportion of pregnancies are full-term? Solution Step 1: Find the z-scores for x = 252 and x = 298. For x = 252: z = 252 − 272 9 = −2.22 For x = 298: z = 298 − 272 9 = 2.89 Step 2: Sketch a normal curve, label the mean, the x-values, and the z-scores, and shade in the area to be found. See Figure 7.16. 252 272 298 z = −2.22 z = 2.89 Figure 7.16 Step 3: Using Table A.2, we find that the area to the left of z = 2.89 is 0.9981 and the area to the left of z = −2.22 is 0.0132. The area between z = −2.22 and z = 2.89 is therefore 0.9981 − 0.0132 = 0.9849. We conclude that the proportion of pregnancies that are full-term is 0.9849.
navidi_monk_elementary_statistics_2e_ch7-9
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