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a. If n = 20 and p = .50, find P(x = 12). b. If n = 20 and p = .30, find P(x > 8). c. If n = 20 and p
= .70, find P(x < 12). d. If n = 20 and p = .90, find P(x ? 16). e. If n = 15 and p = .40, find P(4 ?
x ? 9). f. If n = 10 and p = .60, find P(x ? 7).
Solution
a) n = 20 p = .50 P(x=12) = .120 b) n = 20 p = .30
P(x > 8) = P(x=9) + P(x=10) + P(x=11) + ...+ P(x=20) =
.065 + .031 + .012 + .004 + .001 + .000 = .113 c) n = 20 p = .70
P(x < 12) = P(x=11) + P(x=10) + P(x=9) + ... + P(x=0) =
.065 + .031 + .012 + .004 + .001 + .000 = .113 d) n = 20 p =
.90 P(x < 16) = P(x=16) + P(x=15) + P(x=14) + ...+ P(x=0) =
.090 + .032 + .009 + .002 + .000 = .133 e) n = 15 p = .40 P(4 <
x < 9) = P(x=4) + P(x=5) + P(x=6) + P(x=7) + P(x=8) + P(x=9) =
.127 + .186 + .207 + .177 + .118 + .061 = .876 f) n =
10 p = .60 P(x > 7) = P(x=7) + P(x=8) + P(x=9) + P(x=10) =
.215 + .121 + .040 + .006 = .382

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Binomial probability distribution word problems

  • 1. a. If n = 20 and p = .50, find P(x = 12). b. If n = 20 and p = .30, find P(x > 8). c. If n = 20 and p = .70, find P(x < 12). d. If n = 20 and p = .90, find P(x ? 16). e. If n = 15 and p = .40, find P(4 ? x ? 9). f. If n = 10 and p = .60, find P(x ? 7). Solution a) n = 20 p = .50 P(x=12) = .120 b) n = 20 p = .30 P(x > 8) = P(x=9) + P(x=10) + P(x=11) + ...+ P(x=20) = .065 + .031 + .012 + .004 + .001 + .000 = .113 c) n = 20 p = .70 P(x < 12) = P(x=11) + P(x=10) + P(x=9) + ... + P(x=0) = .065 + .031 + .012 + .004 + .001 + .000 = .113 d) n = 20 p = .90 P(x < 16) = P(x=16) + P(x=15) + P(x=14) + ...+ P(x=0) = .090 + .032 + .009 + .002 + .000 = .133 e) n = 15 p = .40 P(4 < x < 9) = P(x=4) + P(x=5) + P(x=6) + P(x=7) + P(x=8) + P(x=9) = .127 + .186 + .207 + .177 + .118 + .061 = .876 f) n = 10 p = .60 P(x > 7) = P(x=7) + P(x=8) + P(x=9) + P(x=10) = .215 + .121 + .040 + .006 = .382