Question

In a binomial distribution, n=7 and π=.15. Find the probabilities of the following events. (Round your answers to 4 decimal places.)

(a) x=1

Probability=

(b) x≤2

Probability =

(c) x≥3

Probability=

Answer 1

X ~ Bin ( n , )

Where n = 7 , = 0.15

P(X) = ⁿC_x * ^x * ( 1 - )^n-x

a)

P(X = 1) = ⁷C₁ * 0.15¹ * ( 1 - 0.15)⁶

= 0.3960

b)

P(X <= 2) = P(X = 0) + P(X = 1) + (X = 2)

= ⁷C₀ * 0.15⁰ * ( 1 - 0.15)⁷ +⁷C₁ * 0.15¹ * ( 1 - 0.15)⁶ +⁷C₂ * 0.15² * ( 1 - 0.15)⁵

= 0.9262

c)

P(X >= 3) = 1 - P(X <= 2)

= 1 - 0.9262

= 0.0738