Question

Consider a binomial probability distribution with p=0.3 and n = 8. What is the probability of the following? b) exactly three successes less than three successes six or more successes a) P(x = 3) = b) P(x<3)= (Round to four decimal places as needed.) (Round to four decimal places as needed.) c) P(x26)= (Round to four decimal places as needed.)

Answer 1

Solution:

We are given

n = 8

p = 0.3

q = 1 - p = 0.7

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

Part a

P(X=3) = 8C3*0.3^3*0.7^(8 - 3) = 56*0.3^3*0.7^5 = 0.254122

Required probability = 0.2541

Part b

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

P(X<3) = 0.057648 + 0.19765 + 0.296475

(by using binomial table)

P(X<3) = 0.5518

Part c

P(X≥6) = P(X=6) + P(X=7) + P(X=8)

P(X≥6) = 0.010002 + 0.001225 + 0.0000656

(by using binomial table)

P(X≥6) = 0.0113