Here's my question and I also attached the binomial distribution table to help!
According to the CDC, in 2015 15% of high school students rode with a driver (in the last 30 days) who had been drinking alcohol. A random sample 12 high school students was chosen. Assume the distribution is normal. Use the Binomial Distribution Table (PDF, 739 KB) (opens in new window) to find the probabilities. Please note, this question is specifically assessing your ability to use the table to find the probability. You may get a slightly different answer due to rounding if you use a calculator or other technology. 1. At least 11 have ridden with a drunk driver. P(r 15) 2. Less than 4 have ridden with a drunk driver. P(r 4): 3. No more than 2 have ridden with a drunk driver. P(r 2) = 4. Exactly 9 have ridden with a drunk driver. P(r 1 1) = 5. At least 1 have ridden with a drunk driver. P(r 1) 6. Between 2 and 4 (exclusive) have ridden with a drunk driver. P(2 4) =Binomial Probability Distribution Distribution Formula: "Crpq-r This table shows the probability of r successes in n independent trials, each with probability of success p. F P 0.01 0.05 0.10 0.15 0.20 0.25 030 035 040 045 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 2 0 .980 .902 .810 .723 640 .563 490 .423 .360 .303 .250 .203 .160 .123 .090 .063 .040 .023 020 .095 . 180 .255 .010 .002 .320 .375 420 455 .480 495 .500 .495 .480 455 .420 2 .375 .320 .255 000 1 80 002 .010 023 040 .063 090 123 160 .203 .250 .303 .360 423 490 563 .640 .723 .810 .902 0 970 .857 .729 .614 .512 .422 343 .275 .216 .166 .125 .091 .064 043 027 .016 .008 .003 001 .OOD .029 .135 .243 .325 .384 .422 441 .444 .432 .408 .375 .334 .288 .239 . 189 .141 .096 .057 .027 .007 .000 .007 .027 .057 .096 .141 .189 .239 .288 .334 .375 .408 .432 444 .441 .422 .384 .325 000 .243 .135 000 00 1 .003 .OOR .016 .027 .043 064 .091 .125 166 .216 275 143 422 512 614 .729 .857 .961 .815 .656 .522 .410 .316 240 .179 .130 .092 .062 .041 .026 015 .008 .004 .002 .001 039 .000 .000 .171 .292 .368 .410 .422 412 .384 .346 .300 .250 .200 .154 .112 .076 .047 .026 .011 .004 .000 001 .014 .049 .098 .154 .211 256 .311 .346 .368 .375 .368 .346 311 .265 .21 1 .154 .098 .049 .014 .000 .0DO .004 011 .026 .047 076 .112 .154 .200 .250 .300 .346 384 .412 422 .410 .368 .292 000 000 .171 DOO .001 002 004 .008 .015 .026 .041 .062 .092 .130 .179 240 .316 .410 .522 .656 .815 5 951 .774 .590 444 .328 .237 .168 .116 .078 .050 .031 .019 .010 .005 .002 .001 .000 .000 .000 .000 .048 .204 .328 .392 .410 .396 360 .312 .259 .206 .156 .113 .077 .049 .028 .015 .006 002 .000 .000 001 .021 .073 .138 .205 .264 309 .336 .346 .337 .312 .276 .230 .181 .132 .051 024 .008 .001 .000 00 1 .008 .024 .051 .088 .132 . 181 .230 6 .312 .337 .346 336 .309 .264 .205 .138 .073 000 .021 .0DO .000 .002 .006 .015 028 .049 .077 113 .156 .206 .259 312 .360 .396 .410 .392 .328 .204 .000 0DO .000 .OOD .000 .001 .002 .005 .010 .019 .031 .050 .078 .116 .168 237 .328 .444 .590 .774 0 .941 .735 .531 .377 .262 .178 .118 .075 .047 .028 .016 .008 .004 .002 .001 .000 .000 .000 .000 .000 .057 .232 .354 .399 .393 .356 303 .244 .187 .136 .094 .061 .037 020 .010 .004 .002 .000 .000 .000 WN- 001 .031 .098 .176 .246 .297 324 .328 .311 .278 .234 .186 .138 095 .060 .033 .015 .006 .001 .OOD .000 .002 .015 .042 .082 132 .185 .236 .276 .303 .312 .303 .276 236 .185 .132 .082 .042 .000 .000 .015 .00 1 .006 .015 .033 060 .095 .138 .186 .234 .278 .311 328 .324 .297 .246 .176 .098 .031 .000 .000 .000 .000 .002 .004 010 .020 .037 .061 .094 136 .187 244 .303 .356 .393 6 .399 .354 .232 000 000 .000 .000 .000 .000 .001 .002 .004 .008 .016 .028 .047 075 118 .178 .262 377 .531 .735 0 932 .698 .478 .321 .210 .133 .082 .049 .028 .015 .OO8 .004 .002 .001 .000 .000 .000 .000 .000 .000 .066 .257 .372 .396 .367 .311 247 . 185 .131 .087 .055 .032 .017 008 .004 .001 .000 .000 .000 .000 WN- .002 .041 .124 .210 .275 .311 318 .299 .261 .214 .164 .117 .077 047 .025 .012 .004 001 .000 .000 000 .004 .023 .062 115 .173 227 .268 .290 .292 .273 .239 .194 .144 .097 .058 .0.29 011 .003 .000F P 0.01 0.05 0.10 0.15 0.20 0.25 030 035 040 045 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 .000 1003 .011 .0,29 .OS8 .097 .144 . 194 .239 .273 .292 .290 268 .000 .227 .173 .000 .115 062 .023 .001 .004 .004 .012 025 .047 .077 117 .164 .214 .261 299 .000 .000 .000 .318 .311 .000 .275 .000 .001 004 .210 .124 .041 .008 .017 .032 7 .055 .087 131 .185 .000 .000 .247 000 .000 .311 .367 .396 .000 .327 .000 000 .257 00 1 .002 .004 015 .028 049 082 0 .133 .210 .321 .923 .663 .430 .272 478 698 .1 68 .100 058 .032 .017 .008 .004 .002 .001 .000 .075 .000 .279 .383 .000 000 .385 .000 .336 .267 .198 .000 000 .137 .090 .055 .031 .016 .008 003 03 .00 1 .051 .149 .000 .000 .238 .000 .294 .000 .000 .311 296 .259 .209 .157 .109 .070 022 .000 .005 .010 .033 .004 .084 .001 .147 .000 .208 254 .279 .000 000 .279 .257 .219 .172 .124 081 .000 .047 ,023 .000 .005 .009 .018 .003 .046 .000 .087 .136 .188 .000 .232 .263 .273 .263 .232 .188 .000 .000 .087 .000 .136 .046 .003 .018 .009 .023 047 .005 .000 .081 .124 .172 .219 .257 .279 279 .254 .000 .000 ,000 .208 .147 .000 .001 .004 .084 .033 010 .005 .022 .041 .070 .109 .157 209 259 .296 .000 .31 1 .000 .000 .294 .238 .000 .000 .149 .051 .000 .001 .003 .O08 .016 .031 .055 000 .090 .137 ,000 000 .000 .198 .267 ,000 .000 .336 .385 000 .383 .279 000 001 ,002 004 008 .017 032 .058 .914 100 .630 .1 68 .387 .232 .272 .430 663 .134 .075 040 021 .010 .002 .001 .000 .000 .083 .299 .000 .387 .000 .368 .000 .302 .000 .000 .225 .156 .000 .100 .060 .034 .018 .0OR .004 .001 .003 .063 .000 ,000 ,000 .172 .260 .302 ,000 .300 267 .000 .000 .216 .161 .111 .070 .041 .021 010 ,001 .000 .008 .004 .000 .045 .107 .176 .000 .234 267 .000 .000 .272 .251 .212 .164 .116 074 042 .000 .021 .009 .001 .007 .003 .0.28 .001 .066 .117 .172 .219 .251 ).000 .260 .246 .213 .167 .118 .000 .074 .039 .0DO .00 1 .017 .005 .DO5 ,001 .017 .039 .000 074 118 .167 .213 .246 .260 .251 219 .000 .000 .000 .001 .172 .117 .066 .028 .003 .009 021 .001 .042 .074 .116 .164 .212 .251 272 .267 .000 .000 .234 .176 .107 .DOD .045 .008 .001 004 .010 .021 .041 .070 .111 .161 216 .000 .000 .000 .267 .300 .302 .000 .000 .260 .000 .000 .172 .063 .00 1 .004 .DOR .018 .034 .060 .100 .000 . 156 .225 .000 000 .302 .000 .368 .000 .387 .299 .000 .000 .000 .000 .00 1 002 .005 .010 021 .040 10 0 .904 .599 .075 .349 .134 .232 .197 .107 .387 .630 .056 028 .014 .006 .003 001 .000 .000 .000 .315 .000 .000 .091 .387 .347 .000 .268 .000 .188 .121 .000 000 .072 .040 .021 .010 .004 .002 .000 .004 .075 .000 .0DO .194 .000 .276 .302 .000 .000 000 .282 233 .176 121 .076 .044 .023 .011 004 .00 1 .000 .010 .000 .057 .000 .000 .130 .201 .000 000 .250 267 .252 .215 .166 .1 17 .075 .042 .000 .021 .009 .00 1 .003 .01 1 .001 .040 .000 .ORR .146 200 .000 000 .238 .251 .238 .205 .160 111 069 .000 .037 .016 .000 .001 .006 001 000 .026 .000 .058 .103 . 154 .201 .234 .246 .234 .201 .154 6 .000 .000 .000 .103 .001 .058 026 .0OR .006 .016 037 .001 .000 069 .11 1 .160 .205 .238 .251 238 .200 .000 .000 .146 .000 .000 .040 .001 011 001 .003 009 .021 .042 .075 117 .166 .215 252 .267 .000 .000 .250 .000 .201 .000 .130 .000 .000 001 .057 .010 .004 .01 1 .023 .044 .076 121 .176 .233 .000 .282 .000 .000 .302 .276 .000 .000 4 .075 .000 .000 .000 .002 .004 10 .010 021 040 072 .000 .000 000 . 121 .000 .188 .268 .347 ,000 .000 .000 .387 .315 000 .000 001 003 006 014 .028 89 .056 11 .569 314 .107 .167 .197 .349 .ORG $99 .042 .020 009 .004 ,00 1 000 ,000 ,000 1 000 .099 ,000 .329 384 .325 ,000 000 .236 ,OOD .155 093 ,000 000 .052 027 .013 .005 ,002 .001 .000 .000 .000 .000 .000 .000 .000\fF P 0.01 0.05 0.10 0.15 0.20 0.25 030 035 040 045 0.50 055 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 13 .000 000 .000 .000 .000 .000 .0DO .0DO .001 .003 .009 .022 048 .092 .156 .231 .286 .267 .135 14 .000 .000 000 .000 .000 .000 000 .000 .000 .0DO .000 .002 .005 013 .031 .067 .132 .231 .343 .366 15 .000 .000 000 .000 .000 OOO .000 .000 .000 002 005 .013 .035 087 .206 .463 16 0 .831 .440 .185 .074 .028 .010 003 00 1 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .001 .138 .371 .329 .210 .113 .053 023 .009 .003 .00 1 .000 .000 .000 000 .000 .000 .000 .000 .000 .000 010 . 146 .275 .277 .211 .134 .073 035 .015 .006 .002 .001 .000 .000 .000 .000 .000 .000 .000 .001 .000 .036 . 142 .229 .246 .208 .146 .089 .047 .022 .009 .003 .001 000 .000 .000 .000 .000 .000 .000 .000 .006 .051 .131 .200 .225 204 .155 .101 .057 .028 .011 .004 001 .000 .000 .000 .000 .000 .000 .000 .001 .014 .056 .120 .180 210 .201 .162 .112 .067 .034 .014 005 .00 1 .000 .000 .000 .000 .000 6 .000 .000 .003 .018 .055 .110 .165 .198 .198 .168 .122 .075 .039 017 .006 .00 1 .000 .000 .000 .000 .000 .000 .005 .020 .052 .101 .152 .189 -197 .175 -132 .084 044 .019 .006 .001 .000 .000 000 .000 .000 .000 .001 .006 .020 049 .092 .142 .181 .196 .181 .142 092 .049 .020 .006 .001 .000 .000 .000 .0DO .000 .000 .001 006 019 .044 .084 .132 .175 .197 .189 .152 .101 .052 .020 .005 .000 .000 10 .000 .000 .000 .000 .000 .001 006 .017 .039 .075 .122 .068 .198 .198 .165 .110 .055 .018 .003 .000 11 .000 .000 .000 .000 .000 .000 001 .005 .014 .034 .067 112 .162 201 .210 .180 .120 .056 .014 .001 12 .000 .000 .000 .000 .000 .000 000 .001 .004 .011 .028 .057 .101 .155 .204 225 .200 .131 .051 .006 13 .000 .000 .000 .000 .000 .000 000 .000 .001 .003 .009 .022 047 089 .146 .208 .246 .229 142 .036 14 .000 .000 .000 .000 .000 .000 000 .000 .000 .001 .002 .006 015 035 .073 .134 .211 .277 .275 .146 15 .000 .000 .000 .000 .000 .000 000 .000 .000 .000 .000 .001 .003 009 .023 .053 .113 .210 .329 .371 16 .000 000 000 .000 000 000 000 .000 000 .000 .000 000 001 .003 010 .028 .074 .185 .440 818 .358 . 122 039 -012 .003 001 .000 .0DO .000 .000 .000 .000 .000 .0DO .0DO .000 .000 .000 .165 .377 .270 .137 .058 .021 007 .002 .000 .0DO .000 .000 .000 000 .000 .000 .000 .000 .000 .000 .016 .189 .285 .229 .137 .067 028 .010 .003 .001 .000 .000 .000 000 .000 .0DO .000 .000 .000 .000 .001 .060 .190 .243 .205 .134 072 .032 .012 .004 .001 .000 .000 000 .0DO .000 .000 .000 .000 .013 .090 .182 .218 .190 .130 .074 .035 .014 .005 .001 .000 .000 .0DO .000 .000 .000 .000 .000 5 .000 .002 032 .103 .175 .202 .179 .127 .075 .036 .015 .005 .001 000 .000 000 .000 .000 .000 .000 6 .000 .000 009 .045 .109 .169 .192 171 . 124 .075 .036 .015 .005 001 .000 .000 .000 .000 .000 7 .000 .000 .002 .016 .055 .112 .164 .184 .166 . 122 .074 .037 .015 005 .001 -000 .000 .000 .000 .000 .000 .005 .022 .061 .114 .161 .180 .162 .120 .073 035 014 .004 .00 1 .000 .OOD .000 .000 .000 .000 -000 .001 .007 .027 065 .116 .160 .177 -160 .119 .071 034 .012 .003 -000 .000 .000 10 .000 .000 .000 .000 .002 .010 031 .069 .117 . 159 .176 .159 .117 069 .031 .010 -002 .000 .000 .000 11 .000 .000 .000 .000 .000 .003 012 .034 071 .119 .160 .177 .160 .116 .065 .027 .007 .001 .000 .000 12 .000 .000 .0DO .000 2000 .001 004 .014 .035 .073 .120 .162 .180 .161 .114 .061 .022 .005 .000 .OOD 13 .000 .000 .000 .000 .000 .000 001 .005 .015 .037 .074 .122 .166 .184 .164 .112 .055 .016 .002 .000 14 .000 .000 .000 .000 .000 000 .001 .005 .015 .037 .075 .124 .171 .192 .169 .109 .045 .009 .OOD 15 .000 000 000 .000 .000 .000 .000 .000 .001 .005 .015 .036 .075 .127 .179 .202 -175 .103 .032 .002