Question

Binomial Distribution Problem. A study suggested that 70% of internet searches used Google search engine. A sample of 25 searches is studied.

What is the probability that 15 or more searches used Google? For this problem we want just the answer. Please give up to 4 significant decimal places, and use the proper rules of rounding.

Answer 1

Solution:

Given in the question

Probability of success = 0.7

No.of sample = 25

We need to calculate P( X>=15) = P(X=15)+P(X=16)+P(X=17)+P(X=18)+P(X=19)+P(X=20)+P(X=21)+P(X=22)+P(X=23)+P(X=24)+P(X=25)

We will use binomial distribution theorem

P(X=c ) = nCc *(p)^c*(1-p)^(n-c)

P(X>=15) = 25C15*(0.7)^15*(0.3)^10 +25C16*(0.7)^16*(0.3)^9 +25C17*(0.7)^17*(0.3)^8 +25C18*(0.7)^18*(0.3)^7+25C19*(0.7)^19*(0.3)^6+25C20*(0.7)^20*(0.3)^5+25C21*(0.7)^21*(0.3)^4+25C22*(0.7)^22*(0.3)^3+25C23*(0.7)^23*(0.3)^2+25C24*(0.7)^24*(0.3)^1+25C25*(0.7)^25*(0.3)^0

After calculating this long equation we found

P(X>=15) = 0.9022