Consider a binomial experiment with n = 20 and p =.70. if you calculate the binomial probabilities manually, make sure to carry at least 4 decimal digits in your calculations.

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Mathematics

Remington Wolf

16 October, 01:08

Consider a binomial experiment with n = 20 and p =.70. if you calculate the binomial probabilities manually, make sure to carry at least 4 decimal digits in your calculations.

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Beatrice Haas · Answer 1

Answer: f (x) = C (20, x) (0.7) ^x (0.3) ^ (20-x) a) f (12) = C (20,12) (0.7) ^12 (0.3) ^8 = 0.1144 b) f (16) = C (20,16) (0.7) ^16 (0.3) ^4 = 0.1304 c) P (x ≥ 16) = f (16) + f (17) + f (18) + f (19) + f (20) = 0.2375 d) P (x ≤ 15) = 1 - P (x ≥ 16) = 1 - 0.2375 = 0.7625 e) E (x) = np = 20 * 0.7 = 14 f) Var (x) = np (1-p) = 20 * 0.7 * 0.3 = 4.2 ... σ = √4.2 = 2.05