Question

Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and the probability of obtaining a success. Round your answer to four decimal places.

P(X≥2),n=5,p=0.2

Answer 1

SOLUTION:

From given data,

Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and the probability of obtaining a success. Round your answer to four decimal places.

P(X ≥ 2 ),n = 5,p = 0.2

P(X ≥ 2 ) = P(2 < X < 5) = P(X = 2,3,4,5)

P(X ≥ 2 ) = P(X=2)+P(X=3)+P(X=4)+P(X=5)

P(X ≥ 2 ) = ⁵C₂ * 0.2²*(1-0.2)^5-2 +⁵C₃ * 0.2³*(1-0.2)^5-3 +⁵C₄ * 0.2⁴*(1-0.2)^5-4 +⁵C₅ * 0.2⁵*(1-0.2)^5-5

P(X ≥ 2 ) = (10 * 0.2²*0.8³ )+(10 * 0.2³*0.8² )+ (5 * 0.2⁴*0.8¹) + (1 * 0.2⁵*0.8⁰)

P(X ≥ 2 ) = 0.2048 +0.0512+ 0.0064 + 0.00032

P(X ≥ 2 ) = 0.2627

the probability of  P(X ≥ 2 ) = 0.2627