Question

For a sample size of 7 and success rate of 5%, find the probability of:

a)6 successes

b)1 success

c)at least 5 successes

d)more than 5 successes

e)at most 4 successes

Answer 1

X ~ Bin ( n , p)

Where n = 6 , p = 0.05

Binomial probability distribution is

P(X) = nCx * p^x * ( 1 - p)^n-x

a)

P(X = 6) = ⁷C₆ * 0.05⁶ * ( 1 - 0.05)¹

= 0.0000

b)

P(X = 1) = ⁷C₁ * 0.05¹ * ( 1 - 0.05)⁶

= 0.2573

c)

P(C >= 5) = P(X =5) + P(X = 6)

= ⁷C₅ * 0.05⁵ * ( 1 - 0.05)² +⁷C₆ * 0.05⁶ * ( 1 - 0.05)¹

= 0.0000

d)

P(X > 5) = P(X = 6)

^{= 7}C₆ * 0.05⁶ * ( 1 - 0.05)¹

= 0.0000

e)

P(X <= 4) = 1 - P(X > = 5)

= 1 - 0000

= 1