Area- Standard Normal Distribution 0.00 0.01 0.05 L.07 -3.4 0.0003 0.0003 0.0003 1.0005 0/0002 -13 0.00 05 1.0004 0.0004 1 0004 1 0004 0.0003 -32 0,0017 0.0007 0.0006 0,0006 1 1005 0 0005 1 0005 -31 0.0010 0.0009 0.0009 1.0009 0.0108 0.10 08 0.0008 1.0008 0.0007 0.0007 -30 0.0013 010013 0TO013 0.0012 010012 00011 0.0011 10011 0.0010 0 0010 -29 0,0019 0.0018 0,0018 0.00 17 0.0016 0.0016 0.0015 10015 0.0014 0.0014 2.8 0.0026 0.0025 0.0024 0.0023 0.0123 0.0122 0.0021 0.0019 -2.7 0.0035 0.0034 10033 0.0032 010031 0.0029 0 0026 -2.6 0.0047 0.0045 0.0044 0.0043 0.D041 0.00-40 0.0039 10037 1/1036 2.5 0.0062 0.0060 0.0109 1.0037 0.0055 0.0164 10.0052 W051 10049 10048 24 0,0082 0.0080 0.0078 0.0075 0.0073 0,0071 0,0059 0.0068 0 0056 0 0064 -2.3 0,0107 0.0104 0.0102 0.0009 0.0096 0.0194 0.0091 0.0 089 0 0057 10084 0.0139 0.0.136 0.0132 1.0129 0.0125 0.0122 0.0119 0.0113 100110 0,0179 0.0 174 0.0170 0.0166 0,0162 0,0158 0,0154 0 0150 0.0146 10143 0.0228 0.02 22 0.0217 0.0212 0.0207 0.0212 0.0197 1.0192 0.0188 10183 0.0287 070281 0.0274 0.02 68 0.0262 070256 0.0250 0 0244 010239 0.0273 1.8 0.0359 0.0351 0.0344 0.0336 010320 010322 0.0314 10301 010204 1.7 0.0446 0.0436 0.0427 0.0418 0.0409 0.0401 0.0302 010375 0 0367 1.6 0.0548 0.0537 0.0526 0.0516 0.0495 0.0485 0.0475 0.0465 0.0455 1.5 010668 0.0655 170643 0.0630 10606 0,0594 1 0582 10571 1 0559 -14 0.0808 0.0793 0.0778 0.0764 0.0749 0.0735 0.0721 0.0708 010681 13 0.0968 070951 0.0934 1.0918 0.0901 0.0835 0.0869 0.0823 1.2 0.1151 0.1131 0.1112 0.1093 0.1075 0.1056 0.1038 1.1020 1 0985 -1.1 0.1357 0.1335 0.1314 0.1292 0.1271 0.1251 0.1230 0.1210 0.1190 0.1170 -1.0 0.1587 0.1562 0.1539 0.1515 0.1492 0.1469 0.1446 0.1423 0.1401 0.1379 0.1841 0.1814 0.1788 0.1762 0.1736 0.1711 0.1685 0.1660 0.1635 0.1611 -08 0.21 19 0.2090 0.2161 0.2033 0.2105 0.1977 0.1949 0.1922 0-1894 D.1867 -0.7 0.2420 0.2389 0.2358 0.2327 0.2296 0.2266 0.2236 0.2206 0.2177 0.2148 -0.6 0.2743 0.2700 0.2676 0.2643 0.261 1 0.2578 0.2546 0 2514 1 2483 0 2451 0.3085 0.3050 0.3015 0.2981 0.2946 0.2912 0.2877 0.2843 0.2810 0.2776 -0A 0.3446 03409 0.3372 0.3336 0.3300 0.3264 0.3228 0.3192 0.3156 1 3121 -03 0.3821 0.3783 0.3745 0.3707 0,3660 0,3632 0.3504 0.3557 0.3520 0 3483 -0.2 0.4207 0/4168 0.4120 0/4090 0.4052 0.4013 0.3974 0.3936 0.3897 D.3859 -0,1 0.4602 0.4562 0.4522 0.4483 0.4443 0.4404 0.4364 0.4325 0.4286 0.4247 0,5000 0.4060 0,4020 0.4880 0,4840 0,4801 0.4761 0.4721 0.4681 0.4641\fSuppose a simple random sample of size n = 40 is obtained from a population with u = 63 and o = 18. (a) What must be true regarding the distribution of the population in order to use the normal model to compute probabilities regarding the sample mean? Assuming the normal model can be used, describe the sampling distribution x. (b) Assuming the normal model can be used, determine P(x 65.2). Click here to view the standard normal distribution table (page 1)_ Click here to view the standard normal distribution table (page 2). (a) What must be true regarding the distribution of the population? O A. The population must be normally distributed and the sample size must be large. O B. There are no requirements on the shape of the distribution of the population. O C. Since the sample size is large enough, the population distribution does not need to be normal. O D. The population must be normally distributed. Assuming the normal model can be used, describe the sampling distribution x. O A. Approximately normal, with u- = 63 and of = - 40 V18 O B. Approximately normal, with u= = 63 and of = 18 O C. Approximately normal, with u- = 63 and of = - 18 -V40 (b) P(x = 66.4) = ](Round to four decimal places as needed.) (c) P(x =65.2) = (Round to four decimal places as needed.)