جدول التوزيع الطبيعي المعياري لقيم Z السالبة - كتاب الإحصاء - الصف 12 - الفصل 1 - المملكة العربية السعودية

المرفق 2: جدول التوزيع الطبيعي المعياري المعياري لقيم Z السالبة.

Table entry for z is the area under the standard normal curve to the left of z.

TABLE A

Standard normal probabilities

--- SECTION: المرفق 2: جدول التوزيع الطبيعي المعياري لقيم Z السالبة. --- المرفق 2: جدول التوزيع الطبيعي المعياري المعياري لقيم Z السالبة. Table entry for z is the area under the standard normal curve to the left of z. --- SECTION: TABLE A --- TABLE A Standard normal probabilities --- VISUAL CONTEXT --- **DIAGRAM**: Probability Description: A bell-shaped curve illustrating the standard normal distribution. The horizontal axis is labeled 'z' at its center. A portion of the curve to the left of 'z' is shaded in blue, and this shaded area is labeled 'Probability' with an arrow pointing to it. The unshaded area to the right of 'z' is colored yellow. This diagram visually represents that the values in the accompanying table correspond to the cumulative area under the curve to the left of a given Z-score. X-axis: z (Standard Score) Y-axis: Probability Density Data: This diagram is a conceptual illustration, not a data plot. It shows the general shape of a normal distribution and how probability is represented as area under the curve. Context: This diagram is crucial for understanding how to interpret the values in the 'Standard normal probabilities' table. It visually explains that each value in the table represents the cumulative probability from negative infinity up to a given Z-score. **TABLE**: Standard normal probabilities Description: A table providing cumulative probabilities for negative Z-scores in a standard normal distribution. The leftmost column, labeled 'z', lists Z-scores to the first decimal place, ranging from -3.4 to 0.0. The top row lists the second decimal place of the Z-score, from .00 to .09. Each cell in the table contains the probability P(Z < z) for the corresponding Z-score. Table Structure: Headers: z | .00 | .01 | .02 | .03 | .04 | .05 | .06 | .07 | .08 | .09 Rows: Row 1: -3.4 | .0003 | .0003 | .0003 | .0003 | .0003 | .0003 | .0003 | .0003 | .0003 | .0002 Row 2: -3.3 | .0005 | .0005 | .0005 | .0004 | .0004 | .0004 | .0004 | .0004 | .0004 | .0003 Row 3: -3.2 | .0007 | .0007 | .0006 | .0006 | .0006 | .0006 | .0005 | .0005 | .0005 | .0005 Row 4: -3.1 | .0010 | .0009 | .0009 | .0009 | .0008 | .0008 | .0008 | .0007 | .0007 | .0007 Row 5: -3.0 | .0013 | .0013 | .0013 | .0012 | .0012 | .0011 | .0011 | .0011 | .0010 | .0010 Row 6: -2.9 | .0019 | .0018 | .0018 | .0017 | .0016 | .0016 | .0015 | .0015 | .0014 | .0014 Row 7: -2.8 | .0026 | .0025 | .0024 | .0023 | .0023 | .0022 | .0021 | .0021 | .0020 | .0019 Row 8: -2.7 | .0035 | .0034 | .0033 | .0032 | .0031 | .0030 | .0029 | .0028 | .0027 | .0026 Row 9: -2.6 | .0047 | .0045 | .0044 | .0043 | .0041 | .0040 | .0039 | .0038 | .0037 | .0036 Row 10: -2.5 | .0062 | .0060 | .0059 | .0057 | .0055 | .0054 | .0052 | .0051 | .0049 | .0048 Row 11: -2.4 | .0082 | .0080 | .0078 | .0075 | .0073 | .0071 | .0069 | .0068 | .0066 | .0064 Row 12: -2.3 | .0107 | .0104 | .0102 | .0099 | .0096 | .0094 | .0091 | .0089 | .0087 | .0084 Row 13: -2.2 | .0139 | .0136 | .0132 | .0129 | .0125 | .0122 | .0119 | .0116 | .0113 | .0110 Row 14: -2.1 | .0179 | .0174 | .0170 | .0166 | .0162 | .0158 | .0154 | .0150 | .0146 | .0143 Row 15: -2.0 | .0228 | .0222 | .0217 | .0212 | .0207 | .0202 | .0197 | .0192 | .0188 | .0183 Row 16: -1.9 | .0287 | .0281 | .0274 | .0268 | .0262 | .0256 | .0250 | .0244 | .0239 | .0233 Row 17: -1.8 | .0359 | .0351 | .0344 | .0336 | .0329 | .0322 | .0314 | .0307 | .0301 | .0294 Row 18: -1.7 | .0446 | .0436 | .0427 | .0418 | .0409 | .0401 | .0392 | .0384 | .0375 | .0367 Row 19: -1.6 | .0548 | .0537 | .0526 | .0516 | .0505 | .0495 | .0485 | .0475 | .0465 | .0455 Row 20: -1.5 | .0668 | .0655 | .0643 | .0630 | .0618 | .0606 | .0594 | .0582 | .0571 | .0559 Row 21: -1.4 | .0808 | .0793 | .0778 | .0764 | .0749 | .0735 | .0721 | .0708 | .0694 | .0681 Row 22: -1.3 | .0968 | .0951 | .0934 | .0918 | .0901 | .0885 | .0869 | .0853 | .0838 | .0823 Row 23: -1.2 | .1151 | .1131 | .1112 | .1093 | .1075 | .1056 | .1038 | .1020 | .1003 | .0985 Row 24: -1.1 | .1357 | .1335 | .1314 | .1292 | .1271 | .1251 | .1230 | .1210 | .1190 | .1170 Row 25: -1.0 | .1587 | .1562 | .1539 | .1515 | .1492 | .1469 | .1446 | .1423 | .1401 | .1379 Row 26: -0.9 | .1841 | .1814 | .1788 | .1762 | .1736 | .1711 | .1685 | .1660 | .1635 | .1611 Row 27: -0.8 | .2119 | .2090 | .2061 | .2033 | .2005 | .1977 | .1949 | .1922 | .1894 | .1867 Row 28: -0.7 | .2420 | .2389 | .2358 | .2327 | .2296 | .2266 | .2236 | .2206 | .2177 | .2148 Row 29: -0.6 | .2743 | .2709 | .2676 | .2643 | .2611 | .2578 | .2546 | .2514 | .2483 | .2451 Row 30: -0.5 | .3085 | .3050 | .3015 | .2981 | .2946 | .2912 | .2877 | .2843 | .2810 | .2776 Row 31: -0.4 | .3446 | .3409 | .3372 | .3336 | .3300 | .3264 | .3228 | .3192 | .3156 | .3121 Row 32: -0.3 | .3821 | .3783 | .3745 | .3707 | .3669 | .3632 | .3594 | .3557 | .3520 | .3483 Row 33: -0.2 | .4207 | .4168 | .4129 | .4090 | .4052 | .4013 | .3974 | .3936 | .3897 | .3859 Row 34: -0.1 | .4602 | .4562 | .4522 | .4483 | .4443 | .4404 | .4364 | .4325 | .4286 | .4247 Row 35: 0.0 | .5000 | .4960 | .4920 | .4880 | .4840 | .4801 | .4761 | .4721 | .4681 | .4641 Calculation needed: This table is used to find the cumulative probability P(Z < z) for a given negative Z-score 'z'. To use the table, locate the first decimal place of 'z' in the 'z' column, and the second decimal place in the top row. The intersection of the row and column gives the probability. Data: The table shows that as Z-scores increase (become less negative), the cumulative probability increases. The probabilities range from very small values (e.g., .0002 for z = -3.49) to .5000 for z = 0.00. Context: This table is a fundamental tool in statistics for calculating probabilities associated with a standard normal distribution, particularly for hypothesis testing and confidence interval construction when dealing with negative Z-scores. It is used in conjunction with the standard normal curve diagram to visualize the area representing the probability.