Question

5. Your university star basketball player is having a difficult night of free throws. His long range probability of making free throws is 80%, however, tonight he only made 2 out of 4 shots. Fans think he was nervous. Let's use simulation to see how likely it is for him to only make 2 out of 4 shots. Random Assignment: Let numbers 0-7 represent "Making the Shot Let numbers 8, 9 represent "Missing the Shot" Use the random number generator on the calculator OR the random number table to simulate 4 free throws at a time. Record the number of shots he makes in his each series of 4. Repeat the simulation 30 times. (Do not make up these numbers -I can tell if you do! Run the simulation!) Trial Number of Shots Made Trial Number of Shots Made 1 16 17 18 19 20 21 7 22 23 24 9 10 25 26 27 11 12 28 13 29 14 30 15 a. Out of the 30 trials, how many times did our star basketball player make exactly 2 shots? b. What is your experimental probability for the chances he will make exactly 2 out of 4 shots? (Divide your answer from part a by 30.) C. Do you think he was nervous, or is this probability high enough that it may have just been chance at work? 2345ON

Answer 1

Solution: Here concept of simulation using random number table is used.

I have taken starting point from 3rd column of 6th row. I have taken first 4 digit of the random number as a measurement for the number of shots player made out of 4 shots, according to given question. For example for the first trial, first 4 digits are 1,4,0 and 6. Hence, according to the question player made 4 shots out of 4 shots. I repeated this process 30 times by taking next random nubers in order to complete 30 trials.

TABLE 1 - RANDOM DIGITS 11164 21215 10438 36792 73944 3631875061 37674 26320 75100 10431 20418 19228 91792 9179176831 58678 87054 31687 93205 43685 19732 08468 4448266558 37649 0888290870 12462 41810 01806 02977 26236 33266 6658360881 97395 20461 36742 02852 50564 04773 1203251414 82384 38370002498070972605 67497 49563 64208 51486 99756 71325 1287214063 93104 784837271768714 18048 2500504151 4823741701 73117 3324242314 8304921933 9281304763 72875 38605 29341 8074980151 33835 52602 79147 08868 2636064516 1797148478 09610 04638 17141 0922710606 55217 130157290700431 45117 338279287302953 85474 65285 17264 95639 61555 78137 97198 12138 53010 5732738224 29301 99754 3119992558 76404 86210 11808 98768 0468987130 94601 15838 16805 61004 43516 17020 31381 3810934976 65692 98566 29550 68368 049855109237780 4026114479 1284145147 97438 60022 12645 62000 7922508153 84967 645397949374917 28067 62490 24216 16975 59138 29478 9921584987 2875919177 14733 63444 37284 95428 33226 559033160543817 3954271168 5760991510 77904 5965250414 31966 87912 87154 24550 13211 22250 74244 12944 68894 38490 36457 98501 31553 62562 96566 48825 50940 49862 96155 95009 2742972918 0845778134 48407 26061 58754 05326 29621 6658362966 12468 2024514015 04014 357130398003024 126397529171020 17265 41598 64074 64629 63293 5330748766 14544 37134 54714 02401 63228 26831 19386 15457 17999 18306 83403 88827 09834 1133368431 31706 26652 04711 34593 22561 676420520430697 44806 969896840385621 45556 35434 09532 64041 99011 14610 40273 09482 62864 0157382274 81446 32477 17048 9452397444 59904 16936 39384 97551 09620 63932 03091 93039894165279510631 09728 68202 2096302477 55494 39563 82244 343929660717220 51984 1075376272 509859759334320 96990552447069325255 400292328948819 0715960172 81697 09119 7480397303 88701 5138073143 98251 78635 27556 20712 57666 412044758978364 38266 94393 7071353388 79865 92069 46492 615942672958272 81754 14648 77210 12923 5371287771 084331917208320 20839137151059717234 39355 74816 03363 10011 92420 35542 86595 72115 7500486054 41190 10061 19660 03500 65431 16530 05547 10683 88102 30176 5586507304 47010 43233 5702252161 2624718552 294913371232285 64844 3498558036 99137 47482 06204 24138 68412 84750 82976 69395 24272 5781257929 10115 69220 4798146588 41387 87195 16196 04393 29600 07428 58863 3537927922 10982 22807 90127 33341 6300212990 96023 28906 10920 77806 23510 88936 5134370958 96768 7431727176 55013 26937 48174 04197 36074 6531 2629923593 6462957801 10437 43965 12446 15444 49244 47277 11346 15884 68774 48983 20481 5981567248 17076 15344 28131 78910 407798638248454 65269 9123945989453895484777919 41105 43216 12608181678463194058 82458 1513976856 86019 47928 961676437574108 9364309204 9885559051 5649211933 64958 70975 62693 35684 72607 23026 37004 329892484301128 74658 85812 61875 23570 75754 2909040264 8039947254 40135 69916

Table - 2 | Trial Number of Shots made Trial Number of Shots made جراحات | حم | 3| 2| 4| 3| 17 | 18 19 | | | | 4| |هاد و اما 22 23 4| 4 | 3| 24 | | | | | | | 10| 11/ 13| 4 | 14 | | | | 15 | 3 | |

5 (2) - From the above table-2 we find that, out of 30 trials, 4 times our star basketball player made exactly 2 shots. 5(b) Probability - No. of favourable cases Total number of cases No. of favourable cases - 4 Total no. of cases = 30 . Probability - 40 = 0.1333 Experimental probability for the chances that will make exactly 2 out of 4 shots is he 0.1333.

Of The that only probability is not high he was nervous 2 out of 4 shots. enough, so I think that's why he made