Question

8.4.22 :3 Question Help The heights of 1000 students are approximately normally distributed with a mean of 177.7 centimeters and a standard deviation of 7.2 centimeters. Suppose 200 random samples of size 25 are drawn from this population and the means recorded to the nearest tenth of a centimeter. Complete parts (a) through (c) below. Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. 0 Standard Normal Distribution Table (Page 2) H A Standard Normal Distribution Table (Page 1) (a) Determine the mean and standard deviation of the sampling distribution of X. - X The mean is H=U. (Type an integer or a decimal. Do not round.) 2 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 2 .00 .01 0.5000 0.5040 0.5398 0.5438 0.5793 0.5832 0.61790.6217 0.6554 0.6591 0.6915 0.6950 0.7257 0.7291 0.7580 0.7611 0.7881 0.7910 0.8159 0.8186 0.8413 0.8438 0.86430.8665 0.8849 0.8869 0.9032 0.9049 0.9192 0.9207 0.9332 0.0345 0.9452 0.9463 0.9554 0.9564 0.9641 0.9649 0.9713 0.9719 0.9772 0.9778 0.98210.9826 0.9861 0.9864 0.9893 0.9896 0.9918 0.9920 0.9938 0.9940 0.9953 0.9955 0.9965 0.9966 0.9974 0.9975 0.9981 0.9982 0.9987 0.9987 0.9990 0.9991 0.9993 0.9993 0.9995 0.9995 0.9997 0.9997 .00 .01 .02 0.5080 0.5478 0.5871 0.6255 0.6628 0.6985 0.7324 0.7642 0.7939 0.8212 0.8461 0.8686 0.8888 0.9066 0.9222 0.9357 0.9474 0.9573 0.9656 0.9726 0.9783 0.9830 0.9868 0.9898 0.9922 0.9941 0.9956 0.9967 0.9976 0.9982 0.9987 0.9991 0.9994 0.9995 0.9997 .02 .03 0.5120 0.5517 0.5910 0.6293 0.6664 0.7019 0.7357 0.7673 0.7967 0.8238 0.8485 0.8708 0.8907 0.9082 0.9236 0.9370 0.9484 0.9582 0.9664 0.9732 0.9788 0.9834 0.9871 0.9901 0.9925 0.9943 0.9957 0.9968 0.9977 0.9983 0.9988 0.9991 0.9994 0.9996 0.9997 .03 .04 .05 .06 .07 0.5160 0.5199 0.5239 0.5279 0.5557 0.5596 0.5636 0.5675 0.5948 0.5987 0.6026 0.6064 0.6331 0.6368 0.6406 0.6143 0.6700 0.6736 0.6772 0.6808 0.7054 0.7088 0.7123 0.7157 0.7389 0.7422 0.7454 0.7486 0.7704 0.77340.7764 0.7794 0.7995 0.8023 0.8051 0.8078 0.8264 0.8289 0.8315 0.8340 0.8508 0.8531 0.8554 0.8577 0.8729 0.8749 0.8770 0.8790 0.8925 0.8944 0.8962 0.8980 0.9099 0.9115 0.9131 0.9147 0.9251 0.9265 0.9279 0.9292 0.9382 0.9394 0.9406 0.9418 0.9495 0.9505 0.9515 0.9525 0.9591 0.9599 0.9608 0.9616 0.9671 0.9678 0.9686 0.9693 0.9738 0.9744 0.9750 0.9756 0.9793 0.9798 0.9803 0.9808 0.9838 0.9842 0.9846 0.9850 0.9875 0.9878 0.9881 0.9884 0.9904 0.9906 0.9909 0.9911 0.9927 0.9929 0.9931 0.9932 0.9945 0.9946 0.9948 0.9949 0.99590.9960 0.99610.9962 0.9969 0.9970 0.9971 0.9972 0.9977 0.9978 0.9979 0.9979 0.9984 0.9981 0.9985 0.9985 0.9988 0.99890.9989 0.9989 0.9992 0.9992 0.9992 0.9992 0.9994 0.9994 0.9994 0.9995 0.9996 0.9996 0.9996 0.9996 0.9997 0.9997 0.9997 0.9997 .04 .05 .06 .07 .08 .09 0.5319 0.5359 0.0 0.5714 0.5753 0.1 0.6103 0.6141 0.2 0.6480 0.6517 0.3 0.6844 0.6879 0.4 0.7190 0.7224 0.5 0.7517 0.7549 0.6 0.7823 0.7852 0.7 0.8106 0.8133 0.8 0.8365 0.83890.9 0.8599 0.8621 1.0 0.8810 0.8830 1.1 0.8997 0.9015 1.2 0.9162 0.9177 1.3 0.9306 0.9319 1.4 0.9429 0.9441 1.5 0.9535 0.9545 1.6 0.9625 0.9633 1.7 0.9699 0.9706 1.8 0.9761 0.9767 1.9 0.9812 0.9817 2.0 0.9854 0.9857 2.1 0.9887 0.9890 2.2 0.9913 0.9916 2.3 0.9934 0.9936 2.4 0.9951 0.9952 2.5 0.9963 0.9964 2.6 0.9973 0.9974 2.7 0.99800.9981 2.8 0.9986 0.9986 2.9 0.9990 0.9990 3.0 0.9993 0.9993 3.1 0.9995 0.9995 3.2 0.9996 0.9997 3.3 0.9997 0.9998 3.4 .08 .09 -3.4 -3.3 -3.2 -3.1 -3.0 -2.9 -2.8 -2.7 -2.6 -2.5 -2.4 -2.3 -2.2 -2.1 -2.0 -1.9 -1.8 -1.7 -1.6 -1.5 -1.4 -1.3 -1.2 -1.1 -1.0 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 -0.0 7 .00 .01 0.0003 0.0003 0.0005 0.0005 0.00070.0007 0.00100.0009 0.0013 0.0013 0.0019 0.0018 0.0026 0.0025 0.00350.0034 0.0047 0.0045 0.0062 0.0060 0.0082 0.0080 0.0107 0.0104 0.0139 0.0136 0.0179 0.0174 0.0228 0.0222 0.0287 0.0281 0.0359 0.0351 0.0446 0.0436 0.0548 0.0537 0.0668 0.0655 0.0808 0.0793 0.09680.0951 0.1151 0.1131 0.1357 0.1335 0.1587 0.1562 0.1841 0.1814 0.2119 0.2090 0.2420 0.2389 0.2743 0.2709 0.3085 0.3050 0.3446 0.3409 0.3821 0.3783 0.4207 0.4168 0.4602 0.4562 0.50000.4960 .00 .01 . 0.0003 0.0005 0.0006 0.0009 0.0013 0.0018 0.0024 0.0033 0.0044 0.0059 0.0078 0.0102 0.0132 0.0170 0.0217 0.0274 0.0344 0.0427 0.0526 0.0643 0.0778 0.0934 0.1112 0.1314 0.1539 0.1788 0.2061 0.2358 0.2676 0.3015 0.3372 0.3745 0.4129 0.4522 0.4920 .02 .03 0.0003 0.0004 0.0006 0.0009 0.0012 0.0017 0.0023 0.0032 0.0043 0.0057 0.0075 0.0099 0.0129 0.0166 0.0212 0.0268 0.0336 0.0418 0.0516 0.0630 0.0764 0.0918 0.1093 0.1292 0.1515 0.1762 0.2033 0.2327 0.2643 0.2981 0.3336 0.3707 0.4090 0.4483 0.4880 .03 .04 0.0003 0.0004 0.0006 0.0008 0.0012 0.0016 0.0023 0.0031 0.0041 0.0055 0.0073 0.0096 0.0125 0.0162 0.0207 0.0262 0.0329 0.0409 0.0505 0.0618 0.0749 0.0901 0.1075 0.1271 0.1492 0.1736 0.2005 0.2296 0.2611 0.2946 0.3300 0.3669 0.4052 0.4443 0.4840 .04 .05 .00 0.0003 0.0003 0.0004 0.0004 0.0006 0.0006 0.0008 0.0008 0.0011 0.0011 0.0016 0.0015 0.0022 0.0021 0.0030 0.0029 0.0040 0.0039 0.0054 0.0052 0.0071 0.0069 0.0094 0.0091 0.0122 0.0119 0.0158 0.0154 0.0202 0.0197 0.0256 0.0250 0.0322 0.0314 0.0401 0.0392 0.0495 0.0485 0.0606 0.0594 0.0735 0.0721 0.0885 0.0869 0.1056 0.1038 0.1251 0.1230 0.1469 0.1446 0.1711 0.1685 0.1977 0.1949 0.2266 0.2236 0.2578 0.2546 0.29120.2877 0.3264 0.3228 0.3632 0.3594 0.4013 0.3974 0.4404 0.4364 0.4801 0.4761 .05 .06 0 0.0003 0.0004 0.0005 0.0008 0.0011 0.0015 0.0021 0.0028 0.0038 0.0051 0.0068 0.0089 0.0116 0.0150 0.0192 0.0244 0.0307 0.0384 0.0175 0.0582 0.0708 0.0853 0.1020 0.1210 0.1423 0.1660 0.1922 0.2206 0.2514 0.2843 0.3192 0.3557 0.3936 0.4325 0.4721 .07 .00 .09 0.0003 0.0002 0.0004 0.0003 0.0005 0.0005 0.0007 0.0007 0.0010 0.0010 0.0014 0.0014 0.0020 0.0019 0.0027 0.0026 0.0037 0.0036 0.0049 0.0048 0.0066 0.0064 0.0087 0.0084 0.0113 0.0110 0.0146 0.0143 0.0188 0.0183 0.0239 0.0233 0.0301 0.0294 0.0375 0.0367 0.0465 0.0455 0.0571 0.0559 0.0694 0.0681 0.0838 0.0823 0.1003 0.0985 0.1190 0.1170 0.1401 0.1379 0.1635 0.1611 0.1894 0.1867 0.2177 0.2148 0.2483 0.2451 0.2810 0.2776 0.3156 0.3121 0.35200.3483 0.3897 0.3859 0.4286 0.4247 0.4681 0.4641 .08 .09 -3.4 -3.3 -3.2 -3.1 -3.0 -2.9 -2.8 -2.7 -2.6 -2.5 -2.4 -2.3 -2.2 -2.1 -2.0 -1.9 -1.8 -1.7 -1.6 -1.5 -1.4 -1.3 -1.2 -1.1 -1.0 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 -0.0 Enter your answer in the answer box and then click Check Answer.

Answer 1

Solution :

Given that,

mean = $\mu$ = 177.7

standard deviation = $\sigma$ = 7.2

n = 25

$\mu$$\bar x$ = 177.7

$\sigma$$\bar x$ = $\sigma$ / $\sqrt$ n = 7.2 / $\sqrt$ 25 = 1.44