Assume that a procedure yields a binomial distribution with n = 8 trials and a probability of success of p = 0.60. Use a binomial probability table to find the probability that the number of successes x is exactly 4. Click on the icon to view the binomial probabilities table. P(4) = (Round to three decimal places as needed.) Binomial Probabilities Table n Binomial Probabilities P n x .01 .05 .10 .20 .30 .40 .50 60 .70 .80 .90 .95 .99 x n 2 0 .950 .902 .810 .640 .490 .360 .250 .160 .090 .040 .010 .002 0+ 0 2 1 .020 .095 .180 .320 .420 .480 .500 480 420 .320 .180 .095 .020 1 2 0+ .002 .010 .040 .090 .160 .250 360 490 .640 .810 .902 .980 2 3 0 .970 .857 .729 .512 .343 .216 .125 .064 .027 .008 .001 0+ 0+ 0 3 1 029 .135 .243 .384 .441 .432 .375 288 .189 .096 .027 .007 0+ 1 2 0+ .007 .027 .096 .189 .288 .375 432 441 354 243 .135 .029 2 3 0+ 0+ .001 .008 .027 .064 .125 216 .343 512 .729 .857 .970 3 0 .961 .815 .656 .410 .240 .130 .062 026 008 .002 0+ 0+ 0+ 0 1 039 .171 .292 .410 .412 .346 .250 .154 076 .026 .004 0+ 0+ 1 2 .001 .014 .049 .154 .265 .346 .375 346 265 .154 .049 014 .001 2 3 0+ 0+ .004 .026 .076 .154 .250 346 412 410 292 .171 .039 3 0+ 0+ 0+ .002 .008 .026 .062 .130 240 410 656 815 .961 4 5 0 .951 .774 .590 .328 .168 .078 .031 010 .002 0+ 0+ 0+ 0+ 0 1 048 .204 .328 .410 .360 .259 .156 077 028 .006 0+ 0+ 0+ 1 2 .001 .021 .073 .205 .309 .346 .312 230 .132 051 .008 .001 0+ 2 3 0+ .001 .008 .051 .132 .230 .312 346 .309 205 .073 .021 .001 3 4 0+ 0+ 0+ .006 .028 .077 .156 259 360 410 328 204 .048 4 5 0+ 0+ 0+ 0+ .002 .010 .031 078 .168 328 590 .774 .951 5 0 .941 .735 .531 .262 .118 .047 .016 .004 .001 0+ 0+ 0+ 0+ 0 1 .057 .232 .354 .393 .303 .187 .094 .037 010 .002 0+ 0+ 0+ 1 2 .001 .031 .098 .246 .324 .311 .234 .138 .060 .015 .001 0+ 0+ 2 3 0+ .002 .015 .082 .185 .276 .312 276 .185 082 .015 .002 0+ 3 0+ 0+ .001 .015 .060 .138 .234 311 324 246 098 .031 .001 4 5 0+ 0+ 0+ .002 .010 .037 .094 .187 303 .393 354 232 .057 5 6 0+ 0+ 0+ 0+ .001 .004 .016 .047 .118 262 531 .735 .941 6 Binomial Probabilities Table 4 0+ 0+ 0+ .006 .028 .077 .156 259 360 410 328 204 .048 4 5 0+ 0+ 0+ 0+ .002 .010 .031 078 .168 328 590 .774 .951 5 6 0 .941 .735 .531 .262 .118 .047 .016 .004 .001 0+ 0+ 0+ 0+ 0 1 .057 .232 .354 .393 .303 .187 .094 .037 010 .002 0+ 0+ 0+ 1 2 .001 .031 .098 .246 .324 .311 .234 .138 .060 015 .001 0+ 0+ 2 3 0+ .002 .015 .082 .185 .276 .312 276 .185 .052 015 .002 0+ 3 4 0+ 0+ .001 .015 .060 .138 .234 311 324 246 .098 .031 .001 4 5 0+ 0+ 0+ .002 .010 .037 .094 .187 303 393 .354 232 .057 5 6 0+ 0+ 0+ 0+ .001 .004 .016 .047 118 262 531 .735 .941 6 7 0 .932 .698 .478 .210 .082 .028 .008 .002 0+ 0+ 0+ 0+ 0+ 0 7 1 066 .257 .372 .367 .247 -131 .055 017 .004 0+ F 0+ 0+ 0+ 1 2 .002 .041 .124 .275 .318 .261 .164 077 .025 .004 0+ 0+ 0+ 2 3 0+ .004 .023 .115 .227 .290 .273 .194 .097 .029 .003 0+ 0+ 3 4 0+ 0+ .003 .029 .097 .194 .273 290 227 .115 .023 .004 0+ 4 5 0+ 0+ 0+ .004 .025 .077 .164 261 318 275 .124 .041 .002 5 6 0+ 0+ 0+ 0+ .004 .017 .055 .131 247 367 372 257 .066 6 7 0+ 0+ 0+ 0+ 0+ .002 .008 028 .062 210 478 .698 .932 7 8 0 .923 .663 .430 .168 .058 .017 .004 .001 0+ 0+ 0+ 0+ 0+ 0 1 .075 .279 .383 .336 .198 .090 .031 .006 .001 0+ 0+ 0+ 0+ 2 .003 .051 .149 .294 .296 .209 .109 .041 010 001 0+ 0+ 0+ ++ 1 2 3 0+ .005 .033 .147 .254 .279 .219 .124 .047 .009 0+ 0+ 0+ 3 4 0+ 0+ .005 .046 .136 .232 .273 232 .136 .046 .005 0+ 0+ 4 5 0+ 0+ 0+ .009 .047 .124 .219 279 254 .147 .033 .005 0+ 5 6 0+ 0+ 0+ .001 .010 .041 .109 209 296 294 .149 .051 .003 6 7 0+ 0+ 0+ 0+ .001 .008 .031 .090 .198 .336 .383 279 .075 7 8 0+ 0+ 0+ 0+ 0+ .001 .004 017 .058 .168 430 663 .923 8 n x .01 .05 .10 .20 .30 .40 .50 .60 .70 .80 .90 .95 .99 x P NOTE: 0+ represents a positive probability less than 0.0005. -