Hi can someone please help me with these Statistics and process capability questions

so like I do not understand how to calculate them

Also, I don't quite get how to use the Z table please help me and guide me along the way Thank you!!

Please also guide me step by step as I'm very lost as I'm new to this topic

Please go thru slowly... Thank you in advance!!!

3 A professor's exam scores are approximately distributed normally with a mean of 72 and a standard deviation of 15 (i) (ii) (iii) (iv) What is the probability that a student sales an 85 or less? What is the probability that a student scones a 95 or more? What is the probability that a student seems a 58 or less? What is the probability that a student was between 78 and 88? Official (Closed) - Mon Sensitive Official (Closed) - Man Sensitive Tutorial 2: Process Capability Analysis Question 1: Question 2: Machinists A. B and C have machined 1,000 pieces of shafts each and the diameters of work piece data collected show the following results: Machinists A. B and C have machined 1,000 pieces of shafts each and the diameters of work piece a) Calculate the Process Capability Indices Cp & Opt for all three Machinists. data collected show the following results: "b) Sketch the Bell Curves of all three processes. (a) Calculate the Process Capability Indices Cp & Opt for all three Machinists. c) Who is the best Machinist? Why? (b) Sketch the Bell Curves of all three processes. d) Who is the worst Machinist? Why c) Who is the best Machinist? Why? Machinist A Machinist B MachinistC (d) Who is the worst Machinist? Why? 11.50 mm Upper Spec Limit = 11.50 mm Upper SpecLimit = 11.50 mm Machinist B Ma chinist C Upper Spec Limit = Machinist A Lower SpecLint = 10.50 mm Upper Spec Limit = |118.50 mm Upper Spec Limit = 135.50 mm Upper Spec Limit = 120.50 mm Lower Spec Limit = 10.50 mm Lower Spec Limit = 10.50 mm Lower Spec Limit = 105.50 mm Lower Spec Limit = 95.50 mr Lower Spec Limit = 105.50 mm Means 10.75 mm Means 11.10 mm Means 11.08 mm Mean= 115.75 mm Mean= |11475 mm Mean= 111.75 mm Standard Deviations 015 Standard Deviation= 020 Standard Deviation= 0.08 Standard Deviation= 3.05 Standard Deviation= 3.50 Standard Deviation= 2.50 Machinist A: Machinist A: Cp = Cp = Cok Upper = Cok Upper = Cok Lower = Got Lower = Machinist B: Machinist B: Cp = Cp = Got Upper = Gok Upper = Got Lower = Gok Lower = Machinist C: Machinist C: Cp = Cp = Got Upper = Gok Upper = Cok Lower = Got Lower = Machinist A Machinist B Machinist C Machinist A Machinist B Machinist C USL LSL Target USL USL LSL USL LSL Target USL LSL LSL Target LSL Target Target Target USLOfficial (Closed) - Non Sensitive Area for Area for Z- Table Negative Z Positive Z -+2 -5 -4 -3 -21-1 0 +1 +2 +3 +4 +5 Z Z (hundredths) .00 -01 .02 .03 04 05 06 .07 .08 TAIL AREA (tenths) 0.0 5000 .4960 .4920 .4880 -4840 4801 4761 .4721 .4681 .4641 0.1 4602 .4562 .4522 .4483 .4443 4404 .4364 .4325 4286 .4247 0.2 4207 .4168 4129 4090 4052 4013 3974 .3936 3897 3859 0.3 3821 .3783 .3745 3707 3669 3632 .3594 .3557 3520 .3483 0.4 -3446 .3409 .3372 3336 .3300 .3264 .3228 .3192 3156 .3121 0.5 3085 3050 .3015 2981 2946 .2912 2877 2843 2810 2776 0.6 .2743 .2709 .2676 .2643 .2611 .2578 2546 2514 .2483 2451 0.7 2420 .2389 2358 2327 .2297 2266 2236 2207 2177 2148 0.8 2119 .2090 .2061 .2033 .2005 .1977 -1949 .1922 .1894 . 1867 09 .1841 .1814 1788 .1762 .1736 .1711 .1685 1660 1635 .1611 1.0 158 1562 1539 .1515 .1492 1469 1446 1423 1401 1379 1.1 ,1357 .1335 .1314 ..1292 1271 .1251 .1230 .1210 .1190 .1170 1.2 ,1151 .1131 .1112 .1093 1075 .1057 .1038 1020 .1003 0985 1.3 .0968 .0951 .0934 .0918 .0901 1885 .0869 10853 .0838 0823 1.4 0808 0793 0778 0764 .0749 .0735 .0721 0708 .0694 0681 1.5 0668 -0655 .0643 0630 .0618 0606 0594 .0582 .0571 0559 1.6 054 0537 0526 .0516 .0505 .0495 0485 0475 0465 045 1.7 -0446 .0436 .0427 -0418 0409 .040 .0392 0384 0375 0367 1.8 0359 .0351 .0344 0336 0329 .0322 .0314 0307 0301 0294 1.9 -0287 .0281 -0274 .0268 0262 .0256 .0250 .0244 0239 0233 2.0 0228 .0222 -0217 .0212 0207 0202 .0197 .0192 .0183 0183 2.1 .0179 .0174 0170 0166 .0162 0158 0154 0150 .0146 0143 2.2 0139 .0136 -0132 .0129 .0125 0122 .0119 0116 .0113 .0110 2.3 .0107 .0104 0102 .0094 10096 .0094 (0091 .D089 ,0087 10084 2.4 .0062 .0090 .0078 .0075 10073 -0071 .0069 .0068 0066 0064 2.5 0062 0050 0059 0057 0055 .0054 1052 0051 .0049 0048 2.6 .0047 0045 004 0043 .0041 .0040 0039 0038 0037 2.7 .0035 0034 .0033 0032 .0031 .0030 .0029 .0028 .0027 -0026 2.8 10026 0025 102 0023 1023 0022 .0021 0021 0020 0019 7.9 .0019 .0018 .0017 _0017 .0016 .0016 .0015 .0015 -0014 0014 3.0 -0014 0013 0013 0012 0012 0011 0011 0011 0010 0010 3.1 .0010 0009 0009 .0009 1000B .0018 .0008 0006 3.2 -0007 0007 .0006 0006 .0006 .0006 .0005 .0005 .0005 3.3 0005 .0005 .0004 .0004 .0004 0004 0004 40014 3.4 .0003 .0003 0003 .0003 .0003 -0003 0103 DO03 .onn2