Question

(a) Calling 500 people (b) The National Health and records whether they are allow a wote 9.* Calculate the following binomial problebthe or calculating the probability with a calculator h e *P(n.p) - ! where (a) P =6, 10, 8) (b) P(x = 15, n = 17, p = .8) 109 (c) P(Z < 4, n = 15, p = 2) (d) P(x > 2, n = 8, p = .4) 4994 15.000 - 1988 15coo 1 -.76

Answer 1

a) n = 10

p = 0.8

q = 1 - 0.8 = 0.2

P(x = 6) = 10C6 x 0.8⁶ x 0.2⁴

= 0.0881

b) n = 17

p = 0.8

q = 1 - 0.8 = 0.2

P(x = 15) = 17C15 x 0.8¹⁵ x 0.2²

= 0.1914

c) n = 15

p = 0.2

q = 1 - 0.2 = 0.8

P(x < 4) = P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3)

= 0.8¹⁵ + 15x0.2x0.8¹⁴ + 15C2x0.2²x0.8¹³ + 15C3x0.2³x0.8¹²

= 0.6482

d) n = 8

p = 0.4

q = 1 - 0.4 = 0.6

P(x $\geq$ 2) = 1 - [P(x = 0) + P(x = 1)]

= 1 - (0.6⁸ + 8x0.4x0.6⁷)

= 1 - 0.1064

= 0.8936