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 less than 20 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 that,

P = 70% = 0.70

1 - P = 0.30

n = 25

Here, BIN ( n , P ) that is , BIN (25 , 0.70)

then,

n*p = 25* 0.70 = 17.5 > 5

n(1- P) = 25*0.30 = 7.5 > 5

According to normal approximation binomial,

X Normal

Mean = = n*P =17.5

Standard deviation = =n*p*(1-p) = 25*0.70*0.30 = 5.25

We using countinuity correction factor

P(X < a ) = P(X < a - 0.5)

P(x < 19.5) = P((x - ) / < (19.5 - 17.5) / 5.25)

= P(z < 0.873)

0.8087

Probability = 0.8087