using the standard normal camulative probability table

Homework 3 - Quality Control Due Midnight of 10/23/2020 (Friday) 200 points Problem 1 (45 points) An automatic filling machine is used to fill 1-liter bottles of cola. The machine's output is approximately normal with a mean of 1.0 liter and a standard deviation of .01 fter. Output is monitored using means of samples of 25 observations. a. Determine upper and lower control limits that will include roughly 99.74 percent of the sample means when the process is in control. (Do not round intermediate calculations. Round your answers to 3 decimal places.) (25 points) I b. Given the following sample means-1.007, 1.002, .998, 1.003.993, and .994, is the process in control? Why?(10 points) c. Is the process in control given the following sample means-1.003, 999.997, 1.001, 1.002, .998, and 1.004? Why? (10 points) Standard Normal Cumulative Probability Table Cumulative probabilities for NEGATIVE z-values are shown in the following table: Z -3.4 3.3 -3.2 -3.1 -3.0 0.00 0.0003 0.0005 0.0007 0.0010 0.0013 0.01 0.0003 0.0005 0.0007 0.0009 0.0013 0.02 0.0003 0.0005 0.0006 0.0009 0.0013 0.03 0.0003 0.0004 0.0006 0.0009 0.0012 0.04 0.0003 0.0004 0.0006 0.0008 0.0012 0.05 0.0003 0.0004 0.0006 0.0008 0.0011 0.06 0.0003 0.0004 0.0006 0.0008 0.0011 0.07 0.0003 0.0004 0.0005 0.0008 0.0011 0.08 0.0003 0.0004 0.0005 0.0007 0.0010 0.09 0.0002 0.0003 0.0005 0.0007 0.0010 -2.9 -2.8 -2.7 -2.6 -2.5 0.0019 0.0026 0.0035 0.0047 0.0062 0.0018 0.0025 0.0034 0.0045 0.0060 0.0018 0.0024 0.0033 0.0044 0.0059 0.0017 0.0023 0.0032 0.0043 0.0057 0.0016 0.0023 0.0031 0.0041 0.0055 0.0016 0.0022 0.0030 0.0040 0.0054 0.0015 0.0014 0.0014 0.0021 0.0020 0.0019 0.0028 0.0027 0.0026 0.0038 0.0037 0.0036 0.0051 0.0049 0.0048 0.0015 0.0021 0.0029 0.0039 0.0052 0.00de 0.0091 0.0119 0.0154 0.0197 -2.4 -2.3 -2.2 0.0082 0.0107 0.0139 0.0179 0.0228 0.0080 0.0104 0.0136 0.0174 0.0222 0.0078 0.0102 0.0132 0.0170 0.0217 0.0075 0.0099 0.0129 0.0166 0.0212 0.0073 0.0096 0.0125 0.0162 0.0207 -2.1 0.0071 0.0094 0.0122 0.0158 0.0202 0.0068 0.0089 0.0116 0.0150 0.0192 0.0066 0.0087 0.0113 0.0146 0.0188 0.0064 0.0084 0.0110 0.0143 0.0183 -2.0 -1.9 -1.8 -1.7 -1.6 -1.5 0.0287 0.0359 0.0446 0.0548 0.0668 0.0281 0.0351 0.0436 0.0537 0.0655 0.0274 0.0344 0.0427 0.0526 0.0643 0.0268 0.0336 0.0418 0.0516 0.0630 0.0262 0.0329 0.0409 0.0505 0.0618 0.0256 0.0322 0.0401 0.0495 0.0606 0.0250 0.0314 0.0392 0.0485 0.0694 0.0244 0.0307 0.0384 0.0475 0.0582 0.0239 0.0301 0.0375 0.0465 0.0571 0.0233 0.0294 0.0367 0.0455 0.0559 -1.4 -1.3 - 1.2 -1.1 0.0808 0.0968 0.1151 0.1357 0.1587 0.0793 0.0951 0.1131 0.1335 0.1562 0.0778 0.0764 0.0934 0.0918 0.1112 0.1093 0.1314 0.1292 0.1539 0.1515 0.0749 0.0735 0.0721 0.0901 0.0885 0.0869 0.1075 0.1056 0.1038 0.1271 0.1251 0.1230 0.1492 0.1409 0.1446 0.0708 0.0853 0.1020 0.1210 0.1423 0.0004 0.0838 0.1003 0.1190 0.1401 0.0081 0.0823 0.0985 0.1170 0.1379 -0.9 -0.8 -0.7 -0.6 -0.6 0.1841 0.2119 0.2420 0.2743 0.3085 0.1814 0.2090 0.2380 0.2709 0.3050 0.1788 0.1762 0.1736 0.2061 0.2033 0.2005 0.2358 0.2327 0.2296 0.2676 0.2643 0.2611 0.3015 0.2981 0.2046 0.1711 0.1977 0.2266 0.2578 0.2912 0.1085 0.1949 0.2236 0.2546 0.2877 0.1000 0.1635 0.1022 0.1894 02206 02177 0.2514 0.2483 0.2843 0.2810 0.1611 0.1867 0.2148 0 2451 0.2776 -0.4 -0.3 -0.2 -0.1 0.3446 0.3821 0.4207 0.4602 0.5000 0.3400 0.3783 0.4168 0.4502 0.4960 0.3372 0.3745 0.4129 0.4522 0.4920 0.3336 0.3707 0.4000 0.4483 0.4880 0.3300 0.3660 0.4062 0.4443 0.4840 0.3204 0.3632 0.4013 0.4404 0.4801 0.3228 0.3594 0.3974 0.4364 0.4761 0.3192 0.3557 0.3936 0.4325 0.4721 0.3156 0.3620 0.3897 0.4286 0.4681 0.3121 0.3483 0.3850 0.4247 0.4841