1. Only the correct answer is needed. Please round to nearest mile.

A mechanic sells a brand of automobile tire that has a life expectancy that is normally distributed, with a mean life of 31,000 miles and a standard deviation of 2800 miles. He wants to give a guarantee for free replacement of tires that don't wear well. How should he word his guarantee if he is willing to replace approximately 10% of the tires? Click to view page 1 of the table. Click to view page 2 of the table. Tires that wear out by miles will be replaced free of charge. (Round to the nearest mile as needed.) X Standard Normal Table (Page 1) X Standard Normal Table (Page 2) Z 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0 Z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.0 - 3.40.00020.00030.00030.00030.00030.00030.00030.00030. 0.0 0.50000.50400.50800.51200.51600.51990.52390.52790.53 - 3.3 0.00030.00040.00040.00040.00040.00040.00040.00050.( 0.10.53980.54380.54780.55170.55570.55960.56360.56750.57 - 3.20.00050.00050.00050.00060.00060.00060.00060.00060. 0.20.57930.58320.58710.59100.59480.59870.60260.60640.61 - 3.10.00070.00070.00080.00080.00080.00080.00090.00090. 0.3 0.61790.62170.62550.62930.63310.63680.64060.64430.64 - 3.0 0.00100.00100.00110.00110.00110.00120.00120.00130. 0.40.65540.65910.66280.66640.67000.67360.67720.68080.68 -2.90.00140.00140.00150.00150.00160.00160.00170.00180. 0.50.69150.69500.69850.70190.70540.70880.71230.71570.71 - 2.80.00190.00200.00210.00210.00220.00230.00230.00240. 0.60.72570.72910.73240.73570.73890.74220.74540.74860.75 -2.70.00260.00270.00280.00290.00300.00310.00320.00330. 0.70.75800.76110.76420.76730.77040.77340.77640.77940.78 - 2.60.00360.00370.00380.00390.00400.00410.00430.00440. 0.8 0.78810.79100.79390.79670.79950.80230.80510.80780.81 - 2.50.00480.00490.00510.00520.00540.00550.00570.00590. 0.90.81590.81860.82120.82380.82640.82890.83150.83400.83 - 2.40.00640.00660.00680.00690.00710.00730.00750.00780. 1.0 0.84130.84380.84610.84850.85080.85310.85540.85770.85 - 2.30.00840.00870.00890.00910.00940.00960.00990.01020. 1.10.86430.86650.86860.87080.87290.87490.87700.87900.88 - 2.20.01100.01130.01160.01190.01220.01250.01290.01320. 1.20.88490.88690.88880.89070.89250.89440.89620.89800.89 - 2.10.01430.01460.01500.01540.01580.01620.01660.01700. 1.30.90320.90490.90660.90820.90990.91150.91310.91470.91 - 2.0 0.01830.01880.01920.01970.02020.02070.02120.02170. 1.40.91920.92070.92220.92360.92510.92650.92790.92920.93 - 1.90.02330.02390.02440.02500.02560.02620.02680.02740. 1.50.93320.93450.93570.93700.93820.93940.94060.94180.94 - 1.80.02940.03010.03070.03140.03220.03290.03360.03440. 1.60.94520.94630.94740.94840.94950.95050.95150.95250.95 - 1.70.03670.03750.03840.03920.04010.04090.04180.04270. 1.70.95540.95640.95730.95820.95910.95990.96080.96160.96 - 1.60.04550.04650.04750.04850.04950.05050.05160.05260. 1.8 0.96410.96490.96560.96640.96710.96780.96860.96930.96 - 1.50.05590.05710.05820.05940.06060.06180.06300.06430. 1.90.97130.97190.97260.97320.97380.97440.97500.97560.97 -1.40.06810.06940.07080.07210.07350.07490.07640.07780. 2.00.97720.97780.97830.97880.97930.97980.98030.98080.98 -1.30.08230.08380.08530.08690.08850.09010.09180.09340. 2.10.98210.98260.98300.98340.98380.98420.98460.98500.98 - 1.20.09850.10030.10200.10380.10560.10750.10930.11120. 2.20.98610.98640.98680.98710.98750.98780.98810.98840.98 -1.10.11700.11900.12100.12300. 12510. 12710.12920.13140. 2.30.98930.98960.98980.99010.99040.99060.99090.99110.99 - 1.0 0. 13790.14010. 14230.14460.14690.14920.15150.15390. 2.40.99180.99200.99220.99250.99270.99290.99310.99320.99 - 0.90.16110.16350. 16600. 16850.17110.17360. 17620.17880. 2.50.99380.99400.99410.99430.99450.99460.99480.99490.99 - 0.80.18670.18940. 19220. 19490. 19770.20050.20330.20610. 2.60.99530.99550.99560.99570.99590.99600.99610.99620.99 - 0.70.21480.21770.22060.22360.22660.22960.23270.23580. 2.7 0.99650.99660.99670.99680.99690.99700.99710.99720.99 - 0.60.24510.24830.25140.25460.25780.26110.26430.26760. 2.80.99740.99750.99760.99770.99770.99780.99790.99790.99 -0.50.27760.28100.28430.28770.29120.29460.29810.30150. 2.90.99810.99820.99820.99830.99840.99840.99850.99850.99 - 0.40.31210.31560.31920.32280.32640.33000.33360.33720. 3.0 0.99870.99870.99870.99880.99880.99890.99890.99890.99 - 0.30.34830.35200.35570.35940.36320.36690.37070.37450. 3.10.99900.99910.99910.99910.99920.99920.99920.99920.99 - 0.20.38590.38970.39360.39740.40130.40520.40900.41290. 3.20.99930.99930.99940.99940.99940.99940.99940.99950.99 - 0.10.42470.42860.43250.43640.44040.44430.44830.45220. 3.30.99950.99950.99950.99960.99960.99960.99960.99960.99 - 0.0 0.46410.46810.47210.47610.48010.48400.48800.49200. 3.40.99970.99970.99970.99970.99970.99970.99970.99970.99 Z 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0 Z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.0In a large section of a statistics class, the points for the nal exam are normally distributed, with a mean ot 74 and a standard deviation of 9. Grades are assigned such that the top 10% receive A's, the next 20% received B's, the middle 40% receive C's, the next 20% receive D's, and the bottom 10% receive F's. Find the lowest score on the nal exam that would qualify a student for an A, a B, a C, and a D. Click here to view Page 1 of the Standard Normal Table. Click here to view Page 2 of the Standard Normal Table. Standard Normal Table (Page 1) Standard Normal Table (Page 2) z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0 0.0 .I50000.50400.50800.51200.51600.519905239052790.531190. ' 0.1I.53900.54300.54700.55170.55570.55960.56360.56750.57140.' 0.2 I 579305032058710.59100.59480.59870.60260.60640.61030. . I .61 790.621 70.62550529306131310.63680.64060.64430.64800.= . - I .65540.65910.66280.66640.67000.67360.67720.60080.68440. i . I.69150.69500.69050.70190.70540.70880.71230.71570.71900. .- I .72570.72910.73240.73570.73890.74220.74540.74860.75170. . I .75000.76110.76420.76730.77040.77340.77640.77940.78230. .l I 7..8010 79100. 79390. 79670. 79950. 80230. 80510. 00780. 81060.' - I .81 590. 01060. 02120. 82380. 82640. 82890. 831 50. 03400. 83650.' - . I 9032090490906609082090990911 50913109147091620.' . - I .91920.92070922209236092510.92650927909292093060.' . I .93320.93450.93570.9370093820939409406094 1 80.94290. ' . - I .945209463094740.948409495095050951 509525095350. ' . I 955409564095730958209591095990.96080961 60.96250. ' = I 96410. 96490. 96560. 96640. 96710. 96780. 96860. 96930. 96990. ' I .971 30. 97190. 97260. 97320. 97380. 97440. 97500. 97560. 97610. ' . I .98930909609090099010.9904099060990909911 0.99130.' . - I .99100.99200992209925099270992909931099320.99340.' . I 99300.9940099410.994309945099460994809949099510.' . - I.99530.995509956099570995909960099610.9962099630.' . L9965099660.99670.99680.99690.9970099710.9972099730.' ' I ..99740 99750. 99760. 99770. 99770. 99780. 99790. 99790. 99800. ' ' I 990.1.0 99020. 99020. 99830. 99840. 99840. 99850. 99850. 99860. ' . - I .99970.99970.99970.9997099970999709997099970.99970. ' 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0 In a recent study on world happiness, participants were asked to evaluate their current lives on a scale from 0 to 10, where 0 represents the worst possible life and 10 represents the best possible life. The responses were normally distributed, with a mean of 6.2 and a standard deviation of 1.9. Answer parts (a)-(d) below. (a) Find the probability that a randomly selected study participant's response was less than 4. The probability that a randomly selected study participant's response was less than 4 (Round to four decimal places as needed.) (b) Find the probability that a randomly selected study participant's response was between 4 and 6. The probability that a randomly selected study participant's response was between 4 and 6 is (Round to four decimal places as needed.) (c) Find the probability that a randomly selected study participant's response was more than 8. The probability that a randomly selected study participant's response was more than 8 is (Round to four decimal places as needed.)