z-scores|zα
6.2 Areas Under the Standard Normal Curve
Property 4: Almost all the area under the standard normal curve lies between −3 and 3
Because the standard normal curve is the associated normal curve for a standardized normally distributed variable, we labeled the horizontal axis in Fig with the letter z and refer to numbers on that axis as z-scores. For these reasons, the standard normal curve is sometimes called the z-curve
即z-score=-(2.7+0.05),即-2.750时,概率为0.3%
又例如:
Finding the z-score that has a specifified area to its right is often necessary. We have to make this determination so frequently that we use a special notation, zα
因为. Because the area to its right is 0.025, the area to its left is 1 − 0.025 = 0.975, as shown in Fig;Table II contains an entry for the area 0.975; its corresponding z-score is 1.96.Thus, z0.025 = 1.96, as shown in Fig. 6.15(b).
利用对称性:
Because the standard normal curve is symmetric about 0, the z-score on the left is −1.96.Therefore the two required z-scores are ±1.96, as shown in Fig. 6.17(b)
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