Question

A binomial probability experiment is conducted with the given parameters. Use technology to find the probability of x successes in the n independent trials of the experiment. Use the Tech Help button for further assistance. 

n = 8, p = 0.55, x < 4 

P(X<4) = _______ 

Answer 1

X ~ bin(n,p)

Where n = 8 , p = 0.55

P(X) = ⁿC_x p^x (1-p)^n-x

So,

P(X < 4) = P(X <= 3)

= P(X= 0) +P(X= 1) +P(X= 2) +P(X= 3)

= ⁸C₀ * 0.55⁰ * ( 1 - 0.55)⁸ + ⁸C₁ * 0.55¹ * ( 1 - 0.55)⁷ + ⁸C₂ * 0.55² * ( 1 - 0.55)⁶ + ⁸C₃ * 0.55³ * ( 1 - 0.55)⁵

= 0.2604

[ OR using technology,

P(X < 4) = P(X <= 3) = 0.2604  (from calculator) ]

Answer 2

Given that, X is binomial random variable with parameter n = 8 and p = 0.55

X ~ Binomial ( n = 8, p = 0.55)

We want to find, P(X < 4) = P(X <= 3)

Using TI-84 calculator we get,

P( X <= 3) = 0.2604

=> P(X < 4) = 0.2604

Answer 3