1. Round answer to 4 decimal places:

The lengths of lumber a machine cuts are normally distributed with a mean of 99 inches and a standard deviation of 0.4 inch. (a) What is the probability that a randomly selected board cut by the machine has a length greater than 99.18 inches? (b) A sample of 41 boards is randomly selected. What is the probability that their mean length is greater than 99.18 inches? (a) The probability is D. (Round to four decimal places as needed.) About 76% of all female heart transplant patients will survive for at least Cl years. Eighty female heart transplant patients are randomly selected. What is the probability that the sample proportion surviving for at least Cl years will be less than 69%? Assume the sampling distribution of sample proportions is a normal distribution. The mean of the sample proportion is equal to the population proportion and the standard deviation is pq It . equa o n 111e probability that the sample proportion surviving for at least 3 years will be less than 69% is D. (Round to four decimal places as needed.) The height of women ages 20-29 is normally distributed, with a mean of 64.6 inches. Assume o = 2.6 inches. Are you more likely to randomly select 1 woman with a height less than 66.3 inches or are you more likely to select a sample of 25 women with a mean height less than 66.3 inches? Explain. Click the icon to view page 1 of the standard normal table. Click the icon to view page 2 of the standard normal table. What is the probability of randomly selecting 1 woman with a height less than 66.3 inches? (Round to four decimal places as needed.) Standard Normal Table (Page 1) - X X Standard Normal Table (Page 2) 1....: Area .08 .07 .06 .05 .0 .03 .0 .01 .00 .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 -3.4 .0002 .0003 .0003 .0003 .000 0003 .0003 .000 .0003 .0003 0.0 .5000 .5040 .5080 .5120 .5160 5199 .5239 .5279 .5319 .5359 -3.3 .0003 .0004 0004 .0004 0004 .0004 .0004 .0005 0005 .0005 0.1 .5398 .5438 .5478 .5517 .5557 .5596 5636 5675 5714 .5753 - 3.2 .0005 .0005 .0005 .0006 0006 10006 0006 .0007 0007 0.2 .5793 5832 .5871 .5910 .5948 5987 .6026 .6064 .6103 .6141 - 3.1 .0007 .0007 .0008 .0008 0008 0008 .0009 .0009 .0009 .0010 0.3 .6179 6717 6255 .6293 .6331 .6368 .6406 6443 .6480 .6517 - 3.0 .0010 .0010 0OTT 001 1 0011 0012 .0012 .0013 0015 .0013 0.4 6554 6591 6628 6664 .6700 6736 6772 6808 6844 6879 - 2.9 .0014 .0014 .0015 .0015 0016 0016 .0017 .0018 0018 .0019 0.5 .6915 .6950 6985 .7019 .7054 7088 7123 .7157 .7190 .7224 - 2.8 .0019 .0020 0021 0021 0022 0023 .0023 0024 0025 0026 0.6 .7257 .7291 .7324 .7357 7389 .7422 7454 .7486 .7517 .7549 - 2.7 .0026 00 28 0029 .0030 0031 .0052 0033 0034 0035 0.7 .7580 7611 .7642 7673 .7704 7734 1764 .7794 .7823 .7852 - 2.6 .0036 .0037 .0038 .0039 .0040 0041 .0043 .0044 0045 0047 0.8 .7881 .7910 .7939 7967 .7995 8023 8051 8078 8106 .8133 -2.5 .0048 .0049 .0051 .0052 0054 0055 .0057 0059 .0060 0062 0.9 .8159 8186 .8212 8238 .8264 8289 8315 8340 8365 8389 - 2.4 .0064 .0066 .0068 0069 0071 0073 .0075 .0078 0080 .0082 1.0 8413 8438 .8461 .8485 8508 8531 8554 8577 .8599 .8621 -2.3 .0084 .0087 .0089 .0091 .0094 0096 .0099 0102 .0104 0107 1.1 8643 8665 .8686 .8708 8729 8749 8790 8830 0116 8770 8810 - 2.2 .0110 .0113 40119 0122 0125 .0129 .0132 ,0136 0139 1.2 3849 8869 8888 .8907 8925 8944 8962 8980 8997 .9015 - 2.1 .0143 .0146 0150 .0154 0158 0162 .0166 .0170 .0174 0179 1.3 .9032 9049 .9066 9082 9099 9115 .9131 .9147 .9162 .9177 - 2.0 .0183 .0188 0192 .0197 .0202 0207 .0212 0217 .0222 0228 1.4 9192 9207 9222 9236 9251 9265 9279 9292 9306 .9319 - 1.9 .0233 0239 0244 .0250 .0256 0262 0268 0274 0281 .0287 1.5 .9332 .9345 .9357 .9370 9387 9394 .9406 3418 9429 9441 - 1.8 .0294 0301 0307 .0314 .0322 .0329 .0336 0344 0351 .0359 1.6 9452 9463 .9474 9484 9495 9505 9515 9525 .9535 9545 - 1.7 .0367 .0375 .0384 0392 0401 .0409 04 18 0427 .0436 .0446 1.7 95 54 9564 9573 9582 9591 9599 9608 9616 9625 9633 - 1.6 .0455 .0465 .0475 0485 .0495 0505 0516 .0526 0537 0548 9641 9649 9656 2664 9671 9678 9686 9693 9699 9706 - 1.5 .0559 .0571 0582 0594 .0606 0618 .0630 .0643 .0655 .0668 1.9 9713 9719 9726 9732 9738 9744 9750 9756 9761 9767 - 1.4 .0681 .0694 0708 0721 0735 0749 0778 0793 0808 2.0 9772 9778 9783 9788 9793 9803 9808 9812 9817 - 1.3 .0823 .0838 0853 .0869 .0885 .0901 .0918 .0934 .0951 .0968 2.1 9821 9876 9830 9834 9838 9842 9846 9850 9854 9857 - 1.2 0985 .1003 .1020 1038 .1056 .1075 1093 1112 1131 .1151 2.2 9861 9864 .9868 9871 9875 98/8 9881 9884 988/ 9890 - 1.1 1170 .1190 .1210 1230 .1251 .1271 .1292 .1314 1335 .1357 2.3 9893 9896 9898 9901 9904 9900 9909 9911 .9913 9916 - 1.0 .1379 .1401 .1423 1446 .1469 .1492 .1515 .1539 1562 .1587 2.4 9918 9920 9922 9925 9927 9929 9931 2932 9934 9936 - 0.9 .1611 .1635 1660 1685 .1711 1736 1762 .1788 1814 .1841 2.5 2938 9940 9941 9043 9945 9946 9948 3049 9951 9952 - 0.8 .1867 .1894 .1922 1949 .1977 2005 .2033 .2061 2090 .2119 2.6 9953 9955 9956 .9957 .9959 9960 9961 962 9963 .9964 - 0.7 .2148 .2177 2206 .2236 2266 .2296 .2327 .2358 2389 2420 2.7 9965 9956 9967 9968 .9969 997 9971 1972 9973 9974 -0.6 .2451 2483 .2514 2546 .2578 2611 .2643 2676 .2709 .2743 9974 .9975 9976 9977 9977 .9978 .9979 9979 .9980 9981 -0.5 .2776 .2810 2843 .2877 .2912 .2946 .2981 3015 3050 .3085 29 .9981 .9982 .9982 9983 9984 9984 9985 9985 9986 .9986 - 0.4 .3121 .3156 3192 3228 3264 .3300 3336 3372 3409 3446 3.0 9987 9987 9987 9988 9988 9989 9989 9989 9990 9990 - 0.3 .3483 3520 .3557 .3594 .3632 .3669 .3707 .3745 .3783 .3821 3.1 .9990 .9991 9991 9991 9992 .9992 9992 9992 9993 .9993 -0.2 .3859 .3897 3936 .3974 4013 4052 .4090 .4129 4168 4207 3.2 9993 .9993 9994 9994 9994 .9994 9994 9995 9995 .9995 - 0.1 4247 4286 4325 .4364 4404 4443 .4483 4522 4562 4602 3.3 9995 .9995 .9995 9996 .9996 9996 .9996 .9996 9996 .9997 -0.0 4641 4681 4721 4761 4801 4840 4880 .4920 4960 .5000 3.4 .9997 9997 .9997 9997 .9997 .9997 9997 .9997 .9997 9998 Z .09 .08 .07 .06 .05 .04 .03 .02 -01 .00 .00 01 .03 .04 .05 06 .07 .08 .09