8.1

6. The length of human pregnancies is approximately normal with mean u = 266 days and standard deviation o = 16 days. Complete parts (a) through (f). Print Click here to view the standard normal distribution table (page 1).' Click here to view the standard normal distribution table (page 2).2 (a) What is the probability that a randomly selected pregnancy lasts less than 262 days? The probability that a randomly selected pregnancy lasts less than 262 days is approximately 0.4013 (Round to four decimal places as needed.) Interpret this probability. Select the correct choice below and fill in the answer box within your choice. (Round to the nearest integer as needed.) A. If 100 pregnant individuals were selected independently from this population, we would expect pregnancies to last more than 262 days. O B. If 100 pregnant individuals were selected independently from this population, we would expect 40 pregnancies to last less than 262 days. C. If 100 pregnant individuals were selected independently from this population, we would expect pregnancies to last exactly 262 days. (b) Suppose a random sample of 61 human pregnancies is obtained. Describe the sampling distribution of the sample mean length of pregnancies. The sampling distribution of x is (1) with ux = and of = (Round to four decimal places as needed.) (c) What is the probability that a random sample of 61 pregnancies has a mean gestation period of 262 days or less? The probability that the mean of a random sample of 61 pregnancies is less than 262 days is (Round to four decimal places as needed.) Interpret this probability. Select the correct choice below and fill in the answer box within your choice. (Round to the nearest integer as needed.) O A. If 100 independent random samples of size n = 61 pregnancies were obtained from this population, we would expect sample(s) to have a sample mean of exactly 262 days. B. If 100 independent random samples of size n = 61 pregnancies were obtained from this population, we would expect sample(s) to have a sample mean of 262 days or more O C. If 100 independent random samples of size n = 61 pregnancies were obtained from this population, we would expect sample(s) to have a sample mean of 262 days or less. (d) What is the probability that a random sample of 116 pregnancies has a mean gestation period of 262 days or less? The probability that the mean of a random sample of 116 pregnancies is less than 262 days is (Round to four decimal places as needed.) Interpret this probability. Select the correct choice below and fill in the answer box within your choice. (Round to the nearest integer as needed.) A. If 100 independent random samples of size n = 116 pregnancies were obtained from this population, we would expect sample(s) to have a sample mean of 262 days or less. B. If 100 independent random samples of size n = 116 pregnancies were obtained from this population, we would expect sample(s) to have a sample mean of exactly 262 days. O C. If 100 independent random samples of size n = 116 pregnancies were obtained from this population, we would expect sample(s) to have a sample mean of 262 days or more. (e) What might you conclude if a random sample of 116 pregnancies resulted in a mean gestation period of 262 days or less? This result would be (2) - so the sample likely came from a population whose mean gestation period is (3) - 266 days. (f) What is the probability a random sample of size 17 will have a mean gestation period within 11 days of the mean? The probability that a random sample of size 17 will have a mean gestation period within 11 days of the mean is (Round to four decimal places as needed.) 1: Standard Normal Distribution Table (page 1) Are Table V Standard Normal Distribution 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 -3.4 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0002 -3.3 0.0005 0.0005 0.0005 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0003 -3.2 0.0007 0.0007 0.0006 0.0006 0.0006 0.0006 0.0006 0.0005 0.0005 0.0005 -3.1 0.0010 0.0009 0.0009 0.0009 0.0008 0.0008 0.0008 0.0008 0.0007 0.0007 .30 0.0013 0.001 0.0013 0.0012 1.0012 0.0011 1.001 0.0011 0.0010 0.0010 -2.9 0.0019 0.0018 0.0018 0.0017 0.0016 0.0016 0.0015 0.0015 0.0014 0.0014 0.0026 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021 0.0021 0.0020 0.0019 -27 0.0035 0.0034 0.0033 0.0032 0.0031 0.0030 0.0029 0.0028 0.0027 0.0026 0.0047 0.0045 0.0044 0.0043 0.0041 0.0040 0.0039 0.0038 0.0037 0.0036 25 0.006 0.0060 0.0059 0.0057 0.0055 0.0054 0.0052 0.0051 0.0049 0.0048 0.0082 0.0080 0.0078 ).0075 ).0073 0.0071 0.0069 0.0068 0.0066 0.0064 -2.3 0.0107 0.0104 0.0102 0.0099 0.0096 0.0094 0.0091 ).008 0.0087 0.0084 0.0139 0.0136 0.0132 0.0129 0.0125 0.0122 0.0119 0.0116 0.0113 0.0110 0.0179 0.0174 0.0170 0.0166 0.0162 0.0158 0.0154 0.0150 0.0146 0.0143 - 20 0.0228 0.0222 0.0217 0.0212 0.0207 0.0202 0.0197 0.0192 0.0188 0.0183 -1.9 0.0287 0.0281 0.0274 0.0268 0.0262 0.0256 0.0250 0.0244 0.0239 0.0233 -1.8 0.0359 0.0351 0.0344 0.0336 0.0329 0.0322 0.0314 0.0307 0.0301 0.0294 -1.7 0.0446 0.0436 0.0427 0.0418 0.0409 0.0401 0.0392 0.0384 0.0375 0.0367 -1.6 0.0548 0.0537 0.0526 0.0516 0.0505 0.0495 0.0485 0.0475 0.0465 0.0455 -15 0.0668 0.0655 0.0643 0.0630 0.0618 0.0606 0.0594 0.0582 0.0571 0.0559 -1.4 0.0808 0.0793 0.0778 0.0764 0.0749 0.0735 0.0721 0.0694 0.0681 -1.3 0.0968 0.0951 0.0934 0.0918 0.0901 0.0885 0.0869 0.0853 0.0838 0.0823 -1.2 0.1151 0.1131 0.1112 0.1093 0.1075 0.1056 0.1038 0.1020 0.1003 0.0985 -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 -0.9 0.1841 0.1814 0.1788 0.1762 0.1736 0.1711 0.168 0.1660 0.1635 ).1611 -0.8 0.2119 0.2090 0.2061 0.2033 0.2005 0.1977 0.1949 0.1922 0.1894 0.1867 0.2420 0.2389 0.2358 0.2327 0.2296 ).2266 0.2236 0.2206 0.2177 0.2148 -0.6 0.2743 0.2709 0.2676 0.2643 0.2611 0.2578 0.2546 0.2514 0.2483 0.2451 -0.5 0.3085 0.3050 0.3015 0.2981 0.2946 0.2912 0.2877 0.2843 0.2810 0.2776 -0.4 0.3446 0.3409 0.337 0.3336 0.3300 0.3264 0.3228 0.3192 0.315 0.3121 -0.3 0.3821 0.3783 0.3707 0.3669 0.3632 0.3594 0.3557 0.3520 0.3483 -0.2 0.4207 0.4168 0.4129 0.4090 0.4052 0.4013 0.3974 0.3936 0.3897 0.3859 -0.1 0.4602 0.4562 0.4522 0.4483 0.4443 0.4404 0.4364 0.4325 0.4286 0.4247 -0.0 0.5000 0.4960 0.4920 0.4880 0.4840 0.4801 0.4761 0.4721 0.4681 0.4641 : Standard Normal Distribution Table (page 2)