Argentine soccer player Lionel Messi converts 78% of his penalty kicks. Suppose Messi takes six penalty kicks next season. Find the probability that the number he converts is

(a) exactly six,

(b) at most three, and

(c) more than three.

In Exercises 19–26, find the indicated probabilities. If convenient, use technology or Table 2 in Appendix B.

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Table 2-Binomial Distribution This table shows the probability of x successes in n independent trials, each with probability of success p. n x .01 .05 .10 .15 .20 .25 .30 .35 20.980 .902 .810 .723 .640 .563 .490 .423 1.020 .095 .180 .255 .320 .375 .420 .455 1.029 135 .243 .325 .384 422 P .40 .45 .50 .55 .60 .65 .70 .75 .80 .85 .90 .95 .360 .303 .250 .203.160 .123 .090 .063 .040 .023 .010 .002 .480 .495 .500 .495 .480 .455 .420 .375 .320 .255 .180 .095 2 .000 .002 .010 .023 .040.063 .090 .123 .160 .203 .250 .303 .360 .423 .490 .563 .640 .723 .810 .902 3 0.970 .857 .729 .614 .512 .422 .343 .275 .216 .166 .125 .091 .064 .043 .027 .016 .008 .003 .001 .000 441 444 432 .408 .375 .334 .288 .239 .189 .141 .096 .057 .027 .007 2 .000 .007.027 .057 .096 .141 .189 .239 .288 .334 .375 .408 .432 .444 441 422 .384 .325 .243 .135 3 .000 .000 .001 .003 .008 .016 .027 .043 .064 .091 .125 .166 .216 275 .343 .422 .512 .614 .729 .857 4 0961 .815 .656 .522 .410 .316 .240 .179 130 .092 .062 .041 .026 .015 .008 .004 .002 .001 .000 .000 1.039 171 .292 .368 .410 .422 .412 .384 .346 .300 .250 .200 .154 112 .076 .047 .026 .011 .004 .000 2 .001 .014 .049 .098 .154 211 .265 .311 .346 .368 .375 .368 .346 .311 .265 211 .154 .098 .049 .014 .026 .047 .076 .112 .154 .200 .250 .300 .346 .384 .412 422 .410 .368 .292 .171 4 .000 .000 .000 .001 .002 .004 .008 .015 .026 .041 .062 .092 .130 .179 .240 .316 .410 .522 .656 .815 5 0.951 3 .000 .000 .004 .011 774 .590 .444 .328 .237 .168 .116 .078 .050 .031 .019 .010 .005 .002 .001 .000 .000 .000 .000 1.048 204 .328 .392 .410 .396 .360 .312 .259 .206 .156 .113 .077 .049 .028 .015 .006 .002 .000 .000 2 .001 .021 .073 .138 .205 .264 .309 .336 .346 .337 .312 .276 .230 .181 .132 .088 .051 .024 .008 .001 3 .000 .001 .008 .024 .051 .088 .132 .181 .230 .276 .312 .337 .346 .336 .309 .264 .205 .138 .073 .021 4 .000 .000 .000 .002 .006 .015 .028 .049 .077 .113 .156 .206 .259 .312 .360 .396 .410 .392 .328 .204 5 .000 .000 .000 .000 .000 .001 .002 .005 .010 .019 .031 .050 .078 .116.168 .237 .328 .444 .590 .774 6 0.941 735 .531 .377 .262 .178 .118 .075 .047 .028 .016 .008 .004 .002 .001 .000 .000 .000 .000 .000 1.057 .232 .354 .399 .393 .356 .303 .244 .187 .136 .094 .061 .037 .020 .010 .004 .002 .000 .000 .000 2001 .031 .098 .176 .246 .297 .324 .328 .311 .278 .234 .186 .138 .095 .060 .033 .015 .006 .001 .000 3 .000 .002 .015 .042 .082 .132 .185 .236 .276 .303 .312 .303 .276 .236 .185 .132 .082 .042 .015 .002 4 .000 .000 .001 .006 .015 .033 .060 .095 .138 .186 .234 .278 .311 .328 .324 .297 246 .176 .098 .031 5 .000 .000 .000 .000 .002 .004 .010 .020 .037 .061 .094 .136 .187 244 .303 .356 .393 .399 .354 .232 6 .000 .000 .000 .000 .000 .000 .001 .002 .004 .008 .016 .028 .047 .075 .118 .178 .262 .377 .531 .735